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PHYSICS
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FORWARD
PART – 66 and the Acceptable Means of Compliance (AMC) and Guidance Material
(GM) of the European Aviation Safety Agency (EASA) Regulation (EC) No. 2042/2003,
Appendix 1 to the Implementing Rules establishes the Basic Knowledge Requirements
for those seeking an aircraft maintenance license. The information in this Module (01) of
the AMT – Cat A Training Manuals compiled by AESC Aviation Training Center meets or
exceeds the breadth and depth of knowledge subject matter referenced in Appendix 1 of
the Implementing Rules. The order of the material presented is at the discretion of the
editor in an effort to convey the required knowledge in the most sequential and
comprehensible manner. Knowledge levels required for Cat A maintenance licenses
remain unchanged from those listed in Appendix 1 Basic Knowledge Requirements.
Tables from Appendix 1 Basic Knowledge Requirements are reproduced at the beginning
of each module in the series and again at the beginning of each Sub-Module.
Module 01 Syllabus as outlined in PART-66
CERTIFICATION CATEGORY LEVEL
Sub-Module 01 – Matter
1
Nature of matter: the chemical elements, structure of atoms, molecules;
Chemical compounds.
States: solid, liquid and gaseous;
Changes between states.
Sub-Module 02 – Mechanics
Sub-Module 02.1 – Statics

Force, movements and couples, representation as vectors; 1
Centre of gravity;
Elements of theory of stress, strain and elasticity: tension, compression,
shear and torsion;
Nature and properties of solid, fluid and gas;
Pressure and buoyancy in liquids (barometers).
Sub-Module 02.2 – Kinetics 1
Linear movement: uniform motion in a straight line, motion under
constant acceleration (motion under gravity);
Rotational movement: uniform circular motion (centrifugal/ centripetal
forces);
Periodic motion: pendulum movement;
Simple theory of vibration, harmonics and resonance;

Velocity ratio, mechanical advantage and efficiency.
Sub-Module 02.3 – Dynamics
(a) Mass; 1
Force, inertia, work, power, energy (potential, kinetic and total
energy),
heat, efficiency;
(b) Momentum, conservation of momentum; 1

Impulse;
Gyroscopic principles;
Friction: nature and effects, coefficient of friction (rolling resistance).
Sub-Module 02.4 – Fluid Dynamics
(a) Specific gravity and density;
1
(b) Viscosity, fluid resistance, effects of streamlining;
Effects of compressibility on fluids;
Static, dynamic and total pressure: Bernoulli’s Theorem, venture.
Sub-Module 03 – Thermodynamics
2
Temperature thermometers and temperature scales: Celsius,
Fahrenheit and Kelvin; Heat definition;
Contents
MATTER .................................................................................................................................................. 1
NATURE OF MATTER ....................................................................................................................... 2
STRUCTURE OF ATOMS AND FREE ELECTRONS ..................................................................... 4
THE ELECTRONIC STRUCTURE OF ATOMS ............................................................................... 5
STATES OF MATTER ........................................................................................................................ 6
CHANGES BETWEEN STATES ....................................................................................................... 8
UNIFORM MOTION IN A STRAIGHT LINE .............................................................................. 9
MOTION UNDER CONSTANT ACCELERATION ................................................................... 9
MOTION UNDER GRAVITY ............................................................................................................ 10
ROTATIONAL MOVEMENT............................................................................................................. 12
PENDULAR MOTION ....................................................................................................................... 13
SIMPLE THEORY OF VIBRATION, HARMONICS AND RESONANCE ..................................... 14
MECHANICAL ADVANTAGE, VELOCITY RATIO AND EFFICIENCY ....................................... 15
PULLEYS ........................................................................................................................................... 16
SUB-MODULE 02 – MECHANICS ...................................................................................................... 18
STATICS ............................................................................................................................................ 19
SCALARS AND VECTORS.............................................................................................................. 19
STRESS, ELASTICITY AND STRAIN............................................................................................. 20
MOMENTS OF FORCE .................................................................................................................... 23
NATURE AND PROPERTIES OF MATTER .................................................................................. 24
FLUID PRESSURE & HYDRAULICS .............................................................................................. 26
PASCAL’S LAW ................................................................................................................................ 28
MASS ................................................................................................................................................. 30
FORCE AND WEIGHT ..................................................................................................................... 32
WEIGHT ............................................................................................................................................. 32
WORK ................................................................................................................................................ 35
POWER.............................................................................................................................................. 36
NEWTON’S LAWS ............................................................................................................................ 38
KINETIC ENERGY ............................................................................................................................ 40
HEAT .................................................................................................................................................. 42
TOTAL ENERGY............................................................................................................................... 43
MOMENTUM ..................................................................................................................................... 45
CONSERVATION OF MOMENTUM ............................................................................................... 45

IMPULSE ........................................................................................................................................... 45
GYROSCOPIC PRINCIPLES .......................................................................................................... 48
SPECIFIC GRAVITY AND DENSITY .............................................................................................. 49
DENSITY AND SPECIFIC WEIGHT TABLES ................................................................................ 52
PRESSURE ....................................................................................................................................... 54
STATIC, DYNAMIC AND TOTAL PRESSURE .............................................................................. 55
EFFECTS OF COMPRESSIBILITY ON FLUIDS ........................................................................... 56
VISCOSITY ........................................................................................................................................ 57
FLUID RESISTANCE AND EFFECTS OF STRAMLINING .......................................................... 58
STREAMLINING ............................................................................................................................... 59
BERNOULLI’S PRINCIPLE .............................................................................................................. 59
SUB-MODULE 03 - THERMODYNAMICS ......................................................................................... 62
TEMPERATURE ............................................................................................................................... 63
INTRODUCTION ............................................................................................................................... 65
BASE UNITS ..................................................................................................................................... 65
DERIVED UNITS............................................................................................................................... 66
SI SYMBOLS AND PREFIXES ........................................................................................................ 67
MATTER
Nature of matter: the chemical elements, structure of atoms, molecules;
Chemical compounds.
States: solid, liquid and gaseous;
Changes between states.
LEVEL 1: A familiarization with the principal

elements of the subject.
Objectives:
(a) The applicant should be familiar with the basic
(b) The applicant should be able to give a simple
description of the whole subject, using common
words and examples.
(c) The applicant should be able to use typical terms.
1
NATURE OF MATTER
Definition
Matter is defined as anything that occupies space, hence everything that we can see and feel
constitutes matter. It is now universally accepted that matter is composed of molecules, which, in
turn, are composed of atoms.
If a quantity of a common substance, such as water, is divided in half and the half is then divided,
and the resulting quarter divided, and so on, a point will be reached where any further division will
change the nature of the water and turn it into something else.
Molecule
Matter is composed of several molecules. The molecule is the smallest unit of a substance that
exhibits the physical and chemical properties of the substance. All molecules of a particular
substance are exactly alike and unique to that substance.
A molecule consists of a fixed amount of atoms.
● in an element, all atoms of a molecule are the same.
● in a chemical compound, each molecule has atoms from at least two different
elements.
Hydrogen is normally found as a gas. This gas consists of molecules which have two hydrogen
atoms each.
Not all elements form molecules.
Atom
If a molecule of a substance is divided, it will be found to consist of particles called atoms. An
atom is the smallest possible particle of an element.
Element
An element is a single substance that cannot be separated into different substances except by
nuclear disintegration.
There are more than 100 recognized elements, several of which have been artificially created
from various radioactive elements. Common elements are iron, oxygen, aluminum, hydrogen,
copper, lead, gold, silver, and so on. The smallest division of any of these elements will still have
the properties of that element. A compound is a chemical combination of two or more different
elements, and the smallest possible particle of a compound is a molecule. For example, a
molecule of water ( H2O) consists of two atoms of hydrogen and one atom of oxygen. A picture of
a water molecule is illustrated in figure 6.
Compounds
Compounds are pure substances made up of different elements (at least two) which have been
joined together by a chemical reaction. Therefore the atoms are difficult to separate.
Each composition has a fixed number of atoms with a constant relation of the number of
elements.
For example, water always has two hydrogen atoms and one oxygen atom which form a water
molecule.
The properties of a compound are different from the atoms that make it up. Splitting of a
compound is called analysis.
Building of Chemical Compounds
When mixed, some elements form molecules immediately.
Other mixtures of elements need energy, i.e. heat, to form molecules. However, many mixtures of
elements do not form molecules at all.
2
PROTONS, ELECTRONS AND NEUTRONS

Structure of Atoms
Many discoveries have been made that greatly facilitate the study of electricity and
provide new concepts concerning the nature of matter. One of the most important of
these discoveries has dealt with the structure of the atom. It has been found that an
atom consists of infinitesimal particles of energy known as electrons, protons and
neutrons. All matter consists of two or more of these basic components.
The simplest atom is that of hydrogen, which has one electron and one proton, as shown
in figure A.
The structure of an oxygen atom is indicated in figure B.
This atom has eight protons, eight neutrons and eight electrons. The protons and
neutrons form the nucleus of the atom, electrons revolve around the nucleus in orbits
varying in shape from elliptical to circular and may be compared to planets as they move
around the sun.
Charges
A positive charge is carried by each proton, no charge is carried by the neutrons, and a
negative charge is carried by each electron. The charges carried by the electron and the
proton are equal in magnitude but opposite in nature. An atom that has an equal number
of protons and electrons is electrically neutral; that is, the charge carried by the electrons
is balanced by charge carried by the protons.
Ions
It has been explained that an atom carries two opposite charges, protons in the nucleus
have a positive charge, and electrons have a negative charge. When the charge of the
nucleus is equal to the combined charges of the electrons, the atom is neutral, but if the
atom has a shortage of electrons it will be positively charged. Conversely, if the atom
has an excess of electrons, it will be negatively charged. A positively charged atom is
called a positive ion, and a negatively charged atom is called a negative ion. Charged
molecules are called ions, too. It should be noted that protons remain within the nucleus,
only electrons are added or removed from a atom, thus creating a negative or positive
ion.
3
STRUCTURE OF ATOMS AND FREE ELECTRONS

Shells
The path of an electron around the nucleus of an atom describes an imaginary sphere or
shell. Hydrogen and helium atoms have only one shell, but the more complex atoms
have numerous shells. Figure B illustrates this concept. When an atom has more than
two electrons, it must have more than one shell, since the first shell will accommodate
only two electrons. The number of shells in an atom depends on the total number of
electrons surrounding the nucleus.
The atomic structure of a substance is of interest to the electrician because it determines
how well the substance can conduct an electrical current.
Free Electrons
Certain elements, chiefly metals, are known as conductors because an electric current
will flow through them easily. The atoms of these elements give up electrons or receive
electrons in the outer orbit with little difficulty. The electrons that move from one atom to
another are called free electrons. The movement of free electrons from one atom to
another is indicated in figure C, and it will be noted that they pass from the outer shell of
one atom to the outer shell of the next atom. The only electrons shown are those in the
outer orbits.
As shown in figure C, the movement of free electrons does not always constitute electric
current flow. There are often several free electrons randomly drifting through the atoms
of any conductor. It is only when these free electrons move in the same direction that
electric current exists. A power supply, such as a battery, typically creates a potential
difference from one end of a conductor to another. A strong negative charge on one end
of a conductor and a positive charge on the other is the means to create a useful
electron flow.
Electrical Conductivity
An element can be either a conductor, nonconductor (insulator) or semiconductor
depending on the number of electrons in the valance orbit of the materials atoms.
The valance orbit of any atom is the outer most orbit (shell) of that atom. The electrons
in this valance orbit are known as valance electrons. All atoms desire to have their
valance orbit completely full of electrons, and the fewer valance electrons in an atom,
the easier it will accept extra electrons.
Therefore, atoms with fewer than half of their valance electrons tend to easily accept
(carry) the moving electrons of an electric current flow. Such materials are called
conductors. Materials that have more than half of their valance electrons are called
insulators. Insulators will not easily accept extra electrons.
Materials with exactly half of their valance electrons are semiconductors.
Semiconductors have very high resistance to current flow in their pure state, however,
when exact numbers of electrons are added or removed, the material offers very low
resistance to electric current flow.
Figure 1: Atomic Shell and Free Electrons
4
THE ELECTRONIC STRUCTURE OF ATOMS

General
The electrons are arranged in energy levels or shells around the nucleus and with
increasing distance from the nucleus.
Our knowledge about the structure of atoms depends on the mathematical formulations
predicted by Niels Bohr. He suggested that electrons are distributed in orbits and the
number of electrons held in the orbit depends on the number of the orbit. The orbits are
counted outwards from the nucleus. The higher the orbit number, the further the
electrons are from the nucleus.
The electrons in one orbit form a shell.
If the orbit number is ―n‖, then the maximum electrons held in the orbit is given as 2n2.
The first orbit has n = 1, and will hold 2 electrons, the second orbit has n = 2 and is
capable of holding a total of 8 electrons, similarly the third orbit will be able to contain 18
electrons and so on.
Atomic/Proton Number
This is the number of protons in the nucleus.
Mass/Nucleon Number
This is the total number of protons and neutrons in the nucleus
Shells
The shells are lettered from the innermost shell outwards from K to Q.
There are rules about the maximum number of electrons allowed in each shell:
 The 1st shell (K) has a maximum of 2 electrons
 The 2nd shell (L) has a maximum of 8 electrons
 The 3rd shell (M) has a maximum of 18 electrons
 The 4th shell (N) has a maximum of 32 electrons.
Figure 2 Shells
THE CHEMICAL ELEMENTS

General
An element is a pure substance, made up of atoms with the same number of protons.
Isotope
Isotopes of an element is are atom of the same number of protons but different number
of neutrons.
The majority of atoms which have a specific number of neutrons is regarded as normal,
and the minority with a different number of neutrons is regarded as an isotope of this
atom.
5
Some elements have only ―normal― atoms and therefore there are no isotopes of that
element.
Other elements may have two isotopes with different atomic mass.
Isotopes of an element have the same chemical properties but with a different atomic
mass.
Mixtures
Mixtures are compositions of two or more different elements. In nature mixtures appear
in uniform (homogeneous) or no uniform (heterogeneous) form.
Mixtures have the properties of the different elements that make it up.
In mixtures, the elements are easy to separate. For example, heat in a special range of
temperatures is used for distillation to separate oil which change the state of one
element from liquid to gaseous, but the other element stays liquid.
Table of Elements
The ―Table of elements― contains each of the known elements and their corresponding
atomic numbers and atomic masses.
Figure 3 Table of Elements
STATES OF MATTER
General
Matter may exist in one of three physical states:
● Solid
● Liquid or
● Gas.
All matter exists in one of these states.
A physical state refers to the physical condition of a substance and has no affect on a
substances chemical structure. In other words, ice, water and steam are all H2O and the
same type of matter appears in all of these states. All atoms and molecules in matter are
constantly in motion. This motion is caused by heat energy in the material. The degree
of motion determines the physical state of matter.
6
Solid
A solid has a definite volume and shape, and is independent of its container. For
example, a rock that is put into a jar does not reshape itself to form to the jar. In a solid
there is very little heat energy and, therefore, the molecules or atoms cannot move very
far from their relative position.
For this reason a solid is incompressible.
Liquid
Liquids are also considered incompressible. Although the molecules of a liquid are
farther apart than those of a solid, they are still not far enough apart to make
compressing possible. In a liquid the molecules still partially bond together. This bonding
force is known as surface tension and prevents liquids from expanding and spreading
out in all directions. Surface tension is evident when a container is slightly over filled.
Gas
As heat energy is continually added to a material, the molecular movement increases
further until the liquid reaches a point where surface tension can no longer hold the
molecules down. At this point the molecules escape as gas or vapor. The amount of
heat required to change a liquid to a gas varies with different liquids and the amount of
pressure a liquid is under. For example, at a pressure that is lower than atmospheric,
water boils at a temperature less than 100˚C. Therefore, the boiling point of a liquid is
said to vary directly to pressure.
Gases differ from solids and liquids in the fact that they have neither a definite shape nor
volume. Chemically, the molecules in a gas are exactly the same as they were in their
solid or liquid state.
However, because the molecules in a gas are spread out, gases are compressible.
Figure 4 Physical States
7
CHANGES BETWEEN STATES

General
We can use the diagrams shown below, to explain changes of state and the energy
changes involved.
Evaporation & Boiling (liquid to gas)
In evaporation and boiling the highest kinetic energy molecules can escape from the
attractive forces of the other liquid particles. The particles lose any order and become
completely free. Energy is needed to overcome the attractive forces in the liquid and is
taken in from the surroundings. This means heat is taken in (endothermic). Boiling is
rapid evaporation at a fixed temperature called the boiling point and requires continuous
addition of heat.
Evaporation takes place more slowly at any temperature between the melting point and
boiling point and results in the liquid becoming cooler.
Condensing (gas to liquid)
On cooling, gas particles lose kinetic energy and eventually become attracted together
to form a liquid. There is an increase in order as the particles are much closer together
and can form clumps of molecules.
The process requires heat to be lost to the surroundings i.e. heat given out, so
condensation is exothermic.
Figure 5: Boiling and Condensing

Melting (solid to liquid)
When a solid is heated the particles vibrate more strongly and the particle attractive
forces are weakened. Eventually, at the melting point, the attractive forces are too weak
to hold the structure together and the solid melts. The particles become free to move
around and lose their order arrangement.
Energy is needed to overcome the attractive forces, so heat is taken in from the
surroundings and melting is an endothermic process.
Freezing (liquid to solid)
On cooling, liquid particles lose kinetic energy and become more strongly attracted to
each other. Eventually at the freezing point the forces of attraction are sufficient to
remove any remaining freedom and the particles come together to form the ordered solid
arrangement.
Since heat must be removed to the surroundings freezing is an exothermic process.
Figure 6: Melting and Freezing
8
UNIFORM MOTION IN A STRAIGHT LINE

When a body is moving in a straight line with constant speed it is not accelerating. We
say, that it is moving with constant velocity. If a body’s velocity is not constant, it is
accelerating. A body accelerates if it is changing its speed and/or its direction.
When we discuss a body’s straight line motion, then we do not have any change in
direction. In this instance, any acceleration is due to a change in speed.
Special formulas which deal with straight line motion use certain symbols to represent
specific quantities. These symbols are summarized below:
vav = average velocity
t = time
u = initial velocity
v = final velocity
a = acceleration
s = distance covered*
*Note that ―s‖ is the traditional notation for distance in almost all physics textbooks. This
choice reduces confusion with the symbol ―d‖ for derivative, a concept from calculus.
There is a formula dealing with the motion of a body that you have used for many years.
distance = average speed · time
Using our above symbols, we could write:
Formula 1:
s = vav · t
Note: For the velocity we have used the average velocity.
We all know that is is almost impossible to go or drive a distance with always the same
speed. Sometimes we move faster and sometimes we move lowlier. To simplify our
formula we use the average speed.
Assume we go 10 meters within 10 seconds. That mean our speed is 1 m per second
(m/s). For the following 10 meters we need 5 seconds, which mean our speed is 2 m/s. If
we add both values and divide it by two we will get an average speed of 1.5 m/s. In other
words with an average speed of for
seconds, we cover 100 meters,
MOTION UNDER CONSTANT ACCELERATION

Extending our treatment of motion to include the concept of acceleration. Acceleration
(for straight line motion) is the rate of change of speed in time.
We define acceleration (for straight line motion) in the following:
Formula 2:
a =v —u
t
In using this formula, acceleration (a) may be either positive or negative. If final velocity
(v) is less than initial velocity (u), then our value of acceleration (a) turns out to be a
negative number.
When a problem is given to you to solve, be sure to determine which of these three
quantities are given to you, and which quantity is to be found. Choose the formula which
involves these four quantities. If the formula is not solved for the unknown quantity, solve
for this quantity algebraically. Finally substitute the known quantities and solve for the
unknown quantity.
Calculation of Acceleration
An object has an initial speed u and a final speed v. While it is undergoing this change of
speed, it travels a distance s.
In attacking this problem it is wise to write down exactly what is known and what is
unknown.
Formula 3 involves these four quantities.
9
Formula 3:
v2 = u2 + 2a · s
MOTION UNDER GRAVITY
General
On earth, gravity is a force which pulls on every mass. This force causes the weight of a
mass.
Vector
The vector of this force has a clear direction: the middle of the earth.
Acceleration by Gravity
The bigger the mass, the bigger is the force needed to accelerate it with a constant
acceleration.
However, the bigger the mass, the bigger the weight which causes this force.
By this, the acceleration by gravity is the same on small masses and big masses.
It is said that Galileo proved this by an experiment in Pisa (Italy): at the same time he
dropped two bullets with different weight. The hit the ground the same time. While there
are no historical proves for this experiment, the statement has been proved true.
Earth’s Gravity
Accelerations often have the symbol a.
For the acceleration caused by the earth’s gravity, g is used.
The standard gravity is defined as follows:
Converted into the imperial system, the gravity is
However, this value is only correct on the earth’s surface.

The bigger the height, the smaller the force of the gravity.
Free Fall
When things fall to earth, the mass could accelerate faster and faster. But in reality,
bodies are slowed down because of their drag.
Drag depends on surface and form of the object. By this, bombs fall fast and parachutes
fall slowly.
10
Falling Bodies
Here there are some more examples.
If a compact body, such as a stone, is dropped (not thrown) from a height of 100 meters above
the surface of the earth, it will take about 4.5 seconds for the body to reach the ground. It will
have obtained a speed of 44 m/s (160 km/h, 100 mph). At this speed, the effects of air resistance
are still quite negligible.
Above this speed of 160 km/h (100 mph), the effects of air resistance must be observed.
Therefore, we can conclude that the fall of a body from a height of 100 m or less can be
handled quite accurately with the ordinary acceleration formulas. The value of the acceleration
will be 9.81 m/s2 or 32 ft/s2.
Terminal Velocity
If a body falls from a height greater than 100 m above the surface of the earth, the air resistance
becomes very important. As we said, a height of 100 meters corresponds to a fall of 4.5
seconds.
When the time of fall increases to about 8 seconds, the speed of fall has increased in a
non−linear manner from 160 km/h (100 mph) to 185 km/h (115 mph). As the time of fall
increases beyond 8 seconds the speed of fall remains constant at about 185 km/h.
This speed of fall is called the ―terminal velocity‖.
Example:
A body started from rest and has been falling freely for 3 seconds. At what speed is it falling?
U= 0
T= 3 s
a = 9,81 m/s2 v=?
Use formula 2:
v=u+a· t
v = 0 + 9,81 m/s2 ·3s
v = 29 m/s
Figure 8 Free Fall
11
ROTATIONAL MOVEMENT
UNIFORM CIRCULAR MOTION (CENTRIFUGAL AND CENTRIPETAL FORCES)
General
A ball whirled in a circle experiences an acceleration toward the center of the circle. This
can be proven by considering that the ball is continually changing
direction as it moves in a circle.
The ball would ―like― to follow a straight path. For a deviation from the straight path, force
must be applied on it.
Hammer Throwing
A hammer thrower must continually pull towards the center of rotation, applying his full
weight to make the hammer accelerate continually towards the center of rotation to
absorb the centrifugal force. The centrifugal force is caused by the inertia of a rotating
body and tries to draw this body away from the center of rotation.
As soon as the athlete stops applying the force towards the center (she releases the
hammer) the hammer travels in a straight line, at a tangent to the circle.
The acceleration is in the same direction as the force which makes it move in a circle.
This force opposite to the centrifugal force is called centripetal force (from the Latin
meaning ―center seeking―). Since we have a constant change in the direction of the
motion of the hammer, we have a constant acceleration.
This is called centripetal acceleration and can be calculated by the square of the velocity
divided by the radius of the circular path.
For circular motion,
Concerning bodies moving in a circular path the force directed toward the center of the
path must equal the mass of the body times the square of the speed of the body divided
by the radius of the path.
This force is called the centripetal force.
Rotation
Centrifugal
Force
Centripetal
Force
Figure 9 Hammer Throwing
12
PENDULAR MOTION
General
A pendulum is a weight, suspended in the earth’s gravitational field which is free to pivot
at it’s top end. Pendular motion describes the movement which the pendulum will
undergo if it is given a small displacement from it’s vertical
position and is then allowed to swing freely under gravity.
For experimental purposes, a pendulum can be constructed by attaching a small weight
to a piece of non extendible string and suspending the string by it’s top end.
Terminology
When describing pendular motion the angular displacement of the pendulum from it’s
rest position to it’s maximum swing position is known as the angular amplitude and one
complete swing to and fro is known as one oscillation or vibration.
The length of the pendulum is defined as the distance from the pivot point to the center
of gravity of the bob and the time taken to complete one oscillation is referred to as the
periodic time.
PENDULAR MOVEMENT
General
Observations taken during experiments show that, provided the pendulum has a
displacement of only a few degrees, then the periodic time remains constant even as the
movement slows down.
This observation was first made by the physicist Galileo Galilee in Italy in the 17th
century and he was quick to realize that the pendulum could be very useful in the
manufacture of clocks which up to that time were not particularly accurate. It can also be
observed that the mass of the bob makes no difference to the periodic time. This can be
readily seen when two people of different sizes sit on swings in a park and, as long as
the swings are the same length, they will swing with the same periodic time. If, however
we change the length of one of the swings then the shorter one will have a reduced
periodic time compared to the longer one. We can describe this relationship by saying
that the square of the periodic time is proportional to the length of the pendulum.
Or in mathematical terms
Pivot
Pendulum
Length.
Amplitude
Figure 10 Simple Pendulum
Figure 11 Resonance
13
SIMPLE THEORY OF VIBRATION, HARMONICS AND RESONANCE

Vibration
Now we look at reflected waves.
The most common example is the case of waves originating in a disturbance impressed
on a string of definite length i.e. a string that is fixed at both ends. Many musical
instruments depend on such vibrations. If a sinusoidal wave disturbance is impressed on
a very long cord a sinusoidal wave travels continuously along the cord. However, if the
sinusoidal wave meets a fixed end, a reflected wave moves back along the cord.
he wave patterns which are observed are called the normal modes of vibration of the
cord. In the figure below the length of the cord is L. The wavelength in the various
modes of vibration are ßn. The n is the index of the mode. In the equations which follow,
n has an integral value, that is
n = 1, 2, 3, 4.
We can write a general relation as follows:
Zn = 2 · L
Resonance
The vibration where n = 1 is called the fundamental mode of vibration of the body. The
other vibrations are called overtone vibrations. Everybody which can vibrate has a
certain fundamental mode of vibration that has a definite frequency associated with it. If
this frequency is impressed on the body, it will vibrate with a relatively large amplitude.
We say that the body is vibrating in resonance with the impressed frequency.
Aircraft designers must take resonant frequencies into account when designing aircraft
structure. For example, if a component on an aeroplane or helicopter is allowed to
vibrate at its resonant frequency the amplitude of the vibration can become very large
and the component will destroy itself by vibration.
Let us examine the case of a helicopter which has a tail boom with a natural or resonant
frequency of 1Hz. That is, if you were to strike the boom with your fist it would oscillate
once each second. The normal rotational speed of the rotor is 400 rpm and the
helicopter has three blades on its main rotor. Each time a rotor blade moves over the tail
boom the blade is going to cause a downward pulse of air to strike the tail boom. The
designer must determine the speed at which the pulses will be equal to the resonant
frequency of the boom. One cycle per second is equivalent to 60 cycles/minute. Since
each of the three blades causes a pulse each revolution, there will be 3 x 60 or 180
pulses/minute. Therefore a rotor speed of 180 rpm would be critical and the pilot would
be warned against operating at that speed.
Overtone
The boom also has a secondary, or overtone, resonant frequency of twice the
fundamental resonant frequency, 360 rpm would also have to be avoided but would not
be as critical as 180 rpm. The third frequency of concern would be 3 x 180 or 540, but
that is above the rotor operating speed, so is not a problem. The natural frequency of
vibration is also an extremely important consideration in designing the wings, horizontal
and vertical stabilizers of an aircraft. The designer must be certain that the resonant
frequency when the surface is bent is different from that resonant frequency when it is
twisted. If that is not the case, an aerodynamic interaction with the elasticity of the
surface can result in ―flutter‖ which can cause the surface to fracture in a fraction of a
second after it begins.
Harmonics
A harmonic of a wave is a component frequency of the signal that is an integer multiple
of the fundamental frequency.
In the figure below, one harmonic wave is shown. The first harmonic wave is shown for
the given wave length 2L.For example, the fundamental frequency is 25 Hz. The first
harmonic is 50 Hz, the second harmonic is 75 Hz and so on.
14
Figure 11
MECHANICAL ADVANTAGE, VELOCITY RATIO AND EFFICIENCY

General
There is no application of the basic machine that is used more than the gear. The gear is
used in clocks and watches, in automobiles and aircraft, and in just about every type of
mechanical device.
Gears are used to gain mechanical advantage, or to change the direction of movement.
Mechanical Advantage
To gain a mechanical advantage when using gears, the number of teeth on either the
drive gear or driven gear is varied.
For example, if both the drive gear and the driven gear have the identical number of
teeth, no mechanical advantage is gained.
However, if a drive gear has 50 teeth and a driven gear has 100 teeth a mechanical
advantage of 2 is gained. In other words, the amount of power required to turn the driven
gear is reduced by half.
Many machines use a mechanical advantage to change the amount of force required to
move an object. Some of the simplest mechanical advantage devices used are levers,
inclined planes, pulleys and gears.
Mechanical advantage is calculated by dividing the weight, or resistance (R) of an object
by the force used to move the object.
Usually, this force is called ―effort― with the symbol ―E―.
This is seen in the formula:
Mechanical Advantage
A mechanical advantage of 4 indicates that for every 1 newton of force applied, 4

newtons of resistance can be moved.
This advantage is also known as AMA which mean Actual Mechanical Advantage.
The actual mechanical advantage (AMA) is the ratio of the output force to the input
force. The actual mechanical advantage tells us how much easier it is for the worker.
AMA = F0 : Fi
Example 1:
A worker is able to raise a body weighing 300 N. By applying a force of 75 N. What is the
AMA of the machine that he is using?
AMA = F0: Fi
= 300 N : 75 N = 4
15
Velocity Ratio
Another thing to keep in mind is that the revolution or velocity ratio between two gears is
the reverse ratio of their teeth.
Using the earlier example of a drive gear with 50 teeth and a driven gear with 100 teeth,
the gear ratio is 1:2. However, for every revolution of the drive gear the driven gear
makes half a turn. This results in a revolution ratio of 2:1.
To calculate the velocity ratio ( vr) the following formula is used:
If we assume that an ideal machine existed, we would be able to calculate its advantage
by using the same formula as mentioned above. This calculated advantage is then
called IMA which stands for Ideal Mechanical Advantage.
The ideal mechanical advantage (IMA) is the mechanical advantage that would exist if
there were no friction in the machine. It is the ratio of the input distance di to the output
distance do.
IMA = di : d0
Example 2:
A worker applied his force through a distance of 15 m. The load is raised a distance of
2.5 m.
What is the IMA of the machine that he used?
IMA = di : d0
= 15 m : 2.5 m
=6
Efficiency
For comparison of machines it is essential to know the efficiency. That means the
amount of force that is brought IN compared to the amount of force that comes OUT of
the machine.
To make a statement about the mechanical efficiency we can combine both formulas
mentioned above as follows.
Multiplying the resistance (R) of the object that we want to move with the distance we
want to move ( dR) it and dividing both by the effort that is used to move the object
multiplied by the distance to move it ( dE):
mechanical effort
As we usually express efficiency in percent, we multiply the result of the

mechanical effort by 100%:
PULLEYS
General
Pulleys are another type of simple machine that allow you to gain mechanical advantage. A
single fixed pulley is identical to a first class lever. The fulcrum is the center of the pulley and the
arms that extend outward from the fulcrum are identical in length. Therefore, the mechanical
advantage of a single fixed pulley is 1. When using a pulley in this fashion, the effort required to
raise an object is equal to the object’s weight.
If a single pulley is not fixed, it takes on the characteristics of a second class lever. In other
words, both the effort and weight act in the same direction.
When a pulley is used this way, a mechanical advantage of 2 is gained.
16
A common method used to determine the mechanical advantage of a pulley system is to count
the number of ropes that move or support a moveable pulley.
Distance Ratio
Another thing to keep in mind when using pulleys is that as mechanical advantage is gained, the
distance the effort is applied increases. In other words, with a mechanical advantage of 2, for
every 1 meter the resistance moves, effort must be applied to 2 meter of rope.
This relationship holds true wherever using a pulley system to gain mechanical advantage.
Figure 12 Pulleys and Mechanical
17
SUB-MODULE 02 – MECHANICS
STATIC
Forces, moments and couples, representation as
vectors;
Centre of gravity;
Elements of theory of stress, strain and elasticity:
tension, compression, shear and torsion;
Nature and properties of solid, fluid and gas;
Pressure and buoyancy in liquids (barometers).
KINETICS
Linear movement: uniform motion in a straight line, motion under constant acceleration
(motion under gravity);
Rotational movement: uniform circular motion (centrifugal/ centripetal forces);
Periodic motion: pendulum movement;
Simple theory of vibration, harmonics and resonance;
Velocity ratio, mechanical advantage and efficiency.

Objectives:
(a)The applicant should be familiar with the basic
(b)The applicant should be able to give a simple
words and examples.
18
STATICS
SCALARS AND VECTORS
Scalars
In physics, scalars are all quantities which have no direction. Examples are mass, time and
temperature.
Vectors
When geometry is applied for practical tasks, very often vectors are used. A vector helps to
explain effects in a two or three dimensional area.
Each vector consist of two different parts:
● direction
● intensity
In physics, vectors are all quantities which have a direction. Examples are velocity and force.
The direction of an effect is simply shown by the direction of an arrow. It shows the direction of an
effect related to a basic direction, e.g. north.
The intensity is shown by the length of that arrow. By this, you have the possibility to illustrate the
intensity of velocity, force or other quantities.
Addition of Vectors
Vectors which work on the same object can be added.
In most cases, time is an important factor. Sometimes, the vectors act on an object one vector
after the other.
Addition of Velocities
For example, vector 1 shows speed and direction of an airplane. When the airplane changes
direction and speed, vector 2 shows the new speed and the new direction.
When the result should be calculated, you need the angle and the length of each vector.
Figure 14 Addition of Vectors (Velocity)
19
Addition of Forces
When two forces work on an object on the same time, then the vectors start at the same time and
not one after the other.
When the result should be calculated, you need the angle and the length of each vector.
Figure 15 Addition of Vectors (Force)

CENTER OF GRAVITY
General
The form of a body causes its center of gravity, when the body has the same density.
By this you can see if forces will cause a rotation of the body or not. When the sum of forces acts
left of the center of gravity, this will cause a counterclockwise rotation of this body if the body is
not stabilized anyway.
In the figure below you see two forces shown as vectors, which act on a body.
Examples
Engineers try to design a sports car’s center of mass as low as possible to make the car
handle better.
The same is with a human body: the higher the center of gravity, the higher the risk to tumble.
For a flying aircraft, you can calculate the effects of forces on the vertical and horizontal
axes.
STRESS, ELASTICITY AND STRAIN

General
Figure 16 Center of Gravity

20
When an external force acts on a body, it is opposed by an internal force called stress.
Symbol and Unit
The symbol for stress is typically ơ (greek sigma). The unit for stress is
Pa (Pascal).
Formula
Stress is shown as the ratio:
Stress = External Force
Area of applied Force
Structural Integrity
Structural integrity is a major factor in aircraft design and construction. No production aircraft
leaves the ground before undergoing extensive analysis of how it will fly, the stresses it will
tolerate and its maximum safe capability.
Every aircraft is subject to structural stress. Stress acts on an aircraft whether on the ground or in
flight and is defined as a load applied to a unit area of material. Stress produces a deflection or
deformation in the material called strain. Stress is always accompanied by strain.
Current production of general aviation aircraft are constructed of various materials, the primary
being aluminum alloys. Rivets, bolts, screws and special bonding adhesives are used to hold the
sheet metal in place.
Regardless of the method of attachment of the material, every part of the fuselage must carry
a load, or resist a stress placed on it. Design of interior supporting and forming pieces, and
the outside metal skin all have a role to play in assuring an overall safe structure capable of
withstanding expected loads and stresses.
The stress a particular part must withstand is carefully calculated by engineers. The material a
part is made of is also extremely important and is selected by designers based on its known
properties. Aluminum alloy is the primary material for the exterior skin on modern aircraft. This
material possesses a good strength to weight ratio, is easy to form, resists corrosion, and is
relatively inexpensive.
Five Kinds of Stress

There are five basic structural stresses to which aircraft are subjected to:
● Tension
● Compression
● Torsion
● Shear
● Bending
Figure 17
Terms for Behavior of Materials
● Elastic
Material deforms under stress but returns to its original size and shape when the stress is
released. There is no permanent deformation. Some elastic strain, like in a rubber band,
can be large, but in metals it is usually small.
● Brittle
Material deforms by fracturing. Glass is typically brittle.
● Ductile
Materials deforms without breaking. Metals and most plastics are ductile.
● Viscous
21
Materials that deform steadily under stress. Purely viscous materials like liquids deform
under even the smallest stress. Even metals may behave like viscous materials under high
temperatures and pressure. This known as creep and affects plastics far more than metals.
Elasticity
In physics, elasticity is the physical property of a material that returns to its original shape after
the external force that made it deform is removed.
Note that there are limits of the material: when the force is too big, the material may be torn
apart.
Figure 18 Rubber Band
Strain
Stress is a force within an object that opposes an applied external force. Strain is the measurable
amount of deformation that is caused by stress.
Hooke’s law states that if strain does not exceed the elastic limit of a body, it is directly
proportional to the applied stress. This fact allows beams and springs to be used as measuring
devices.
For example, as force is applied to a hand torque wrench, its deformation or bending, is directly
proportional to the strain it is subjected to. Therefore, the amount of torque deflection can be
measured and used as an indication of the amount of stress applied to a bolt.
Figure 19 Torque Wrench
22
MOMENTS OF FORCE
General
Consider the diagrams below.
The distance between the point and the position where the force attacks is named r. This is,
because when the force is applied and the tool moves it will move in a circle with the radius r.
We define torque as the force (F) applied to a body that is provided at a point
(0) multiplied by the distance r from the pivot point to the place where the force is applied and
multiplied by the sine of the angle ɵ between r and F.
For torque, we will use the Greek letter for Tau. The distance or lever arm is symbolized by
the letter r.
Defining the equation:
From the diagram below we note that the angle ɵ = 90 ˚. This is by far the most common case.
Since sin 90 ˚ = 1, this common case reduces to the more simple equation:
Remember that in those cases where ɵ is not 90 ˚, the full equation must be used.
Symbols and Unit
The symbol for torque is typically , the Greek letter tau (small letter). When it is called moment,
it is commonly denoted M.
Also note that the SI unit for torque is Nm (Newton meter). Other units are the lb.ft or lb.in.
Figure 20 Torque
COUPLES
General
A ―couple‖ is a pair of forces of magnitude F that are equal and opposite but applied at points
separated by distance d perpendicular to the forces. The combined moment of the forces
produces a torque Fd on the object on which they act.
Examples
Example 1
An example is the cutting of an internal thread with a tap and tap wrench. The force applied at
one end of the wrench handle, multiplied by the distance to the center of rotation is just half of
the torque felt at the tap itself, since there is an equal torque applied at the other wrench
handle.
Torque applied by a couple:
● One of the forces (F) x distance to center of rotation (r) x 2
● One of the forces (F) x distance between the forces (d) = Fd Example 2
23
Another example is the forces applied to a car steering wheel.
Figure 21 Control Wheel
NATURE AND PROPERTIES OF MATTER

General
All matters exists in one of three states − Solid, Liquid or Gas. The following characterizes the
three states: solid, liquid and gas.
SOLID
FLUID
1. The greatest forces of attraction are between the particles in a solid and they pack
together in a neat and ordered arrangement.
2. The particles are too strongly held together to allow movement from place to place but the
particles vibrate about there position in the structure.
3. With increase in temperature, the particles vibrate faster and more strongly as they gain
kinetic energy.
The Properties of a Solid
● Solids have the greatest density (heaviest) because the particles are closest together.
● Solids cannot flow freely like gases or liquids because the particles are strongly held in
fixed positions.
● Solids have fixed surface and volume (at a particular temperature) because of the strong
particle attraction.
24
● Solids are extremely difficult to compress because there is no real ―empty‖ space between
the particles.
● Solids will expand a little on heating but nothing like as much as liquids because of the
greater particle attraction restricting the expansion (contract on cooling). The expansion is
caused by the increased strength of particle vibration.
1. Much greater forces of attraction between the particles in a liquid compared to gases, but
not quite as much as in solids.
2. Particles quite close together but still arranged at random throughout the container, there
is a little close range order as you can get clumps of particles clinging together temporarily.
3.Particles moving rapidly in all directions but more frequently colliding with each other than
in gases.
4.With increase in temperature, the particles move faster as they gain kinetic energy.
The Properties of a Fluid
● Fluids have a much greater density than gases (heavier) because the particles are
much closer together.
● Fluids flow freely despite the forces of attraction between the particles but fluids are not
as free as gases.
● Fluids have a surface, and a fixed volume (at a particular temperature) because of the
increased particle attraction, but the shape is not fixed and is merely that of the container
itself.
● Fluids are not readily compressed because of the lack of empty space between the
particles.
● Fluids will expand on heating (contract on cooling) but nothing like as much as gases
because of the greater particle attraction restricting the expansion. When heated, the liquid
particles gain kinetic energy and hit the sides of the container more frequently, and more
significantly, they hit with a greater force, so in a sealed container the pressure produced
can be considerable.
GAS
1.Almost no forces of attraction between the particles which are completely free of each other.
2.Particles widely spaced and scattered at random throughout the container so there is no order
in the system.
3.Particles moving rapidly in all directions, frequently colliding with each other and the side of the
container.
4.With increase in temperature, the particles move faster as they gain kinetic energy.
The Properties of a Gas
 Gases have a low density (light) because the particles are so spaced out in the container
25
(density = Mass ÷ Volume).

 Gases flow freely because there are no effective forces of attraction between the
particles.
 Gases have no surface, and no fixed shape or volume, and because of lack of particle
attraction, they spread out and fill any container.
 Gases are readily compressed because of the empty space between the particles.
 If the container volume can change, gases readily expand on heating because of the
lack of particle attraction, and readily contract on cooling. On heating, gas particles gain
kinetic energy and hit the sides of the container more frequently, and more significantly,
they hit with a greater force. Depending on the container situation, either or both of the
pressure or volume will increase (reverse on cooling).
 The natural rapid and random movement of the particles means that gases readily spread
or diffuse. Diffusion is fastest in gases where there is more space for them to move and
the rate of diffusion increases with increase temperature.
FLUID PRESSURE & HYDRAULICS
Fluid Mechanics
A fluid is any substance that flows or conforms to the outline of a container. Both liquids and
gases are fluids that follow many of the same rules. However, for all practical purposes, liquids
are considered incompressible, while gases
are compressible.
Much of the science of flight is based on the principle of fluid mechanics. For example, the air that
supports an aircraft in flight and the liquid that flows in hydraulic systems both transmit force
through fluid mechanics.
Fluid Pressure
The pressure exerted by a column of liquid is determined by the height of the column and is not
affected by the volume of the liquid.
This pressure is named static pressure.
Symbol and Unit
The symbol for pressure is typically p, from the English word ―Pressure―. The pascal (Pa) is
the SI unit of pressure.
Formula
Example 1
Water has the mass of 998,6 kg per m3.
If you stack 100,000 cubic centimeters (0,1 m3) of water vertically in a column with a base of
one square centimeter, the column would extend 100,000 cm (1,000 m) high and would have
a weight w = 980 N.
There would also be a pressure, or force per unit area of 980 N per cm2 at the bottom of the
column. This is 9800 kN per m2 or 9800 kPa.
26
Example 2
Gasoline has a specific gravity of 0.72, which means its weight is 72% that of water, or 750
kg per cubic meter.
Therefore, a column with a base of 1 square centimeter and 1,000 meters high results in a
pressure of 706 N per cm2.
The pressure exerted by a column of liquid is determined by the height of the column and is not
affected by the volume of the liquid.
Figure 22 Fluid Pressure
Relationship of Force, Pressure & Head

In dealing with fluids, forces are usually considered in relation to the areas over which they are
applied. As previously discussed, a force acting over a unit area is a pressure, and pressure can
alternately be stated in pounds per square inch or in terms of head, which is the vertical height of
the column of fluid whose weight would produce that pressure.
In most of the applications of fluid power, applied forces greatly outweigh all other forces, and the
fluid is entirely confined. Under these circumstances it is customary to think of the forces involved
in terms of pressures. Since the term head is encountered frequently in the study of fluid power, it
is necessary to understand what it means and how it is related to pressure and force.
Terms in General Use
At this point you need to review some terms in general use.
● Gravity head, when it is important enough to be considered, is sometimes referred to as
head.
● The effect of atmospheric pressure is referred to as atmospheric pressure. (Atmospheric
pressure is frequently and improperly referred to as suction.)
● Inertia effect, because it is always directly related to velocity, is usually called velocity
head.
● Friction because it represents a loss of pressure or head, is usually referred to as friction.
Example 1
Gravity head causes a water column lasting on objects in the water. The weight of the water
column causes static pressure.
The interior of the submarine has the same pressure like the surface. So, a differential
pressure exists. Beyond the limit, it will crush the submarine.
27
Example 2
As internal pressure the kraken has the same pressure as the water around him. When the
sailing ship pulls him out quickly, the static pressure surrounding him is too low and the
kraken will burst.
Figure 23 Static Pressure

PASCAL’S LAW
General
Pascal’s Law explains that when pressure is applied to a confined liquid, the liquid exerts an
equal pressure at right angles to the container that encloses it.
Formula
You can find the amount of force (F) produced by a hydraulic piston by multiplying the area (A) of
the piston by the pressure (p) exerted by the fluid.
This is expressed in the formula F = A · p
Formula
For example, assume a cylinder is filled with a liquid and fitted with a piston with A = one square
centimeter. When a force of 1 N is applied to the piston, the resulting pressure of the confined
liquid is 1 N/cm2 everywhere in the container.
For example, when 5 MPa (725 psi) of fluid pressure is supplied to a cylinder with a piston area
of 10 cm2, 5,000 N of force is generated.
To determine the area needed to produce a given amount of pressure, divide the force produced
by the pressure applied.
Force (N) = Pressure (P) · Area (m2)
F = P ·A
To calculate the Area which is needed to generate a specific pressure, then you must divide
the available force F by the designated pressure p.
28
Advantage
Since the shape of a container has no effect on pressure, connecting one cylinder to a large
cylinder results in a gain in mechanical advantage.
For example, a cylinder with a 1 square centimeter piston is connected to a cylinder with a 10
square centimeter piston. When 5 N of force is applied to the smaller piston, the resulting
pressure inside both cylinders is 50 kPa (7,25 psi). This means that the piston in the larger
cylinder has an area of 10 cm2, and 50 kPa of pressure acts on every square inch of the
piston, the resulting force applied to the larger piston is 50 N.
When gaining mechanical advantage this way it is important to note that the pistons do not
move the same distance. In the previous example, when the small piston moves inward 5
cm, it displaces 5 cm3 of fluid. When this is spread out over the 10 cm2 of the larger piston,
the larger piston only moves 0.5 cm.
The pressure produced in a hydraulic cylinder acts at right

angles to the cylinder.
A mechanical advantage may be obtained in a hydraulic system by using a piston

with a small area to force fluid into a cylinder with a larger piston. For example,
when applying a force of 1 pound to a 1 square inch piston, you push upward against
the 10 square inch piston with a force of 10 pounds.
Figure 24 Pascal’s Law
BUOYANCY IN LIQUIDS
The Archimedes Principle
The Archimedes Principle states that when an object is submerged in a liquid, the object
displaces a volume of liquid equal to its volume and is supported by a force equal to the weight of
the liquid displaced. The force that supports the
object is known as the liquids ―buoyant force‖.
29
Liquids
If the object immersed has a specific gravity that is less than liquid, the object displaces its own
weight of the liquid and floats.
Gases
The effect of buoyancy is not only present in liquids, but also in gases. Hot air balloons are able
to rise because they are filled with heated air that is less dense than the air they displace.
Example
For example, when a 100 cubic centimeters block with the weight w = 10 N is attached to a
spring scale and lowered into a full container of water, 100 cubic centimeters of water
overflows out of the container.
The weight of 100 cm2 of water is 0.98 N, therefore the buoyant force acting on the block is
0.98 N.
The spring scale reads 9.02 N.
A body immersed in
a fluid is buoyed up
by a force equal to
the weight of the
fluid it displaces. Figure 25 Archimedes Principle
MASS
General
In physics the term for what we have up to now referred to as the amount of substance or matter
is ―mass‖.
Mass is a SI basic quantity.
Atomic Mass Unit
A natural unit for mass is the mass of a proton or neutron. This unit has a special name the
―Atomic Mass Unit‖ (amu). This unit is useful in those sciences which deal with atomic and
nuclear matter.
In measuring the mass of objects which we encounter daily, this unit is much too small and
therefore very inconvenient. For example, the mass of a bowling ball expressed in amus would
be about 4,390,000,000,000,000,000,000,000,000 amu.
30
One kilogram equals 602,000,000,000,000,000,000,000,000 amu (6.02 x 1026) Since one amu is
the mass of a proton or neutron we know immediately that a kilogram of anything has this
combined number of protons and neutrons contained in it.
Symbol and Unit
The symbol of the mass is m.
The kilogram (kg) is the SI unit of mass.
Imperial Unit
US-Americans use lb for ―Pound―. The unit lb is derived from the latin word ―libra―.
The conversion:
1 lb = 0,45359237 kg
Definition
The mass of an object is described as the amount of matter in an object and is constant
regardless of its location.
For example, an astronaut has the same mass on earth as when in space. However, an
astronaut’s weight is much less on the moon than it is on earth.
Another definition sometimes used for mass is the measurements of an objects resistance to
change its state of rest to motion. This is seen by comparing the force required to move a big
jet as compared to a small single engine aircraft.
Because the jet has a greater mass, it has a greater resistance to change.
Acceleration of Gravity
A realistic menas to find the mass of an object is the following: divide the weight of the
object by the acceleration of gravity.
On earth, this acceleration is:
● 9.8 m/s2 in the metric system
● 32.2 ft/s2 in the imperial system.
Figure 26 Astronaut on the Moon
31
FORCE AND WEIGHT

FORCE
General
Work, power, force & motion are important concepts of physics.
As an aircraft maintenance technician, you must understand these concepts and be able to use
the associated formulae to fully comprehend simple machines like pulleys, levers or gears.
Force
The word ―force‖ generally denotes a push or a pull. When a body is acted upon by a resultant
force it will begin to move. If the body is already moving a force may alter its speed, direction or
bring it to rest. We therefore define force as follows:
Force is that which changes a body’s state of rest or of uniform motion in a straight line.
Symbol and Unit
The symbol for Force is typically F, from the english word ―Force―. The newton (N) is the SI unit of
force.
Formula
Force = F
Mass = m
Acceleration = a
F=m·a
Figure 27 Force
WEIGHT
General
Weight is defined as the gravitational pull of the earth on a given body. This is a force.
The direction of this force is regarded toward the geometrical center of the earth.
Physicists are very careful to distinguish between ―mass & weight‖.
● The mass of an object is the same wherever this object is in the universe. The mass of an
astronaut is the same if he is on the earth, on the moon, in a spaceship or some place in the
milky way galaxy.
● If the astronaut is standing on the earth surface, he has a weight.
● If the astronaut is not on the earth but is in a space station orbiting the earth, he is
weightless.
● If the astronaut is on the moon, we speak of its ―weight on moon‖, the gravitational pull of the
moon on the astronaut.
The greater the mass of an object on the surface of the earth, the greater is the weight of this
object. These two quantities are approximately proportional to each other as long as the body
remains on the earth’s surface. The word ―approximately‖ refers to the fact that the pull of the
32
earth on a body of a given mass varies slightly with the position of the body on the earths surface.
The
pull of the earth on the body is greater at the poles ( 9.83m/s²) and slightly smaller
Formula
Weight = w
Mass = m
Gravity = g
w=m·g
Please not that this is special case for force.
The general formula for force is
F=m·a
Example
For example, a body has a mass of 100 kg.
Its weight at the North Pole is 983,22 N and its weight at a place on the equator is 978,03 N.
at other places on the earth, like the equator ( 9, 78 m/s²).
This is for three reasons:
● the earth is not a perfect shaped bullet
● the earth does not have the same density everywhere
● the earth rotates.
However, we usually neglect this slight difference and calculate with an average value of
9.81m/s²
Symbol fur Quantity and Unit
The symbol for this special force is typically w, for ―Weight―.
The newton (N) is the SI unit of force.
FORCE =
MASS•ACCELERAT
ION
1 daN = 10 Figure 28 Weight

N
FRICTION
NATURE AND EFFECTS
When a body rests on a horizontal surface or is dragged or rolled on such a surface there is
always contact between the lower body surface and the horizontal surface. This contact results in
friction. Friction is work done as the
33
surfaces rub against each other. This work heats the surface and always results in wasted work.
We need to define a force known as the normal force. A body resting on a horizontal surface
experiences two forces, the downward force due to the gravitational pull of the earth on the body
(weight of the body), and the upward push of the surface itself on the body (the normal force).
The weight (w) and the normal force (N) are equal to each other. There are three kinds of
friction:
● Starting friction
● Sliding friction
● Rolling resistance
Starting friction
It is present at the instant when a body, which has been at rest, just begins to move under the
application of a force. Sometimes this instant when the body begins to slide is called ―break
away‖.
Sliding friction
It is present as a body is sliding over another surface. Sliding friction is present when the surface
of the body and the surface on which it slides are moving relative to each other.
ROLLING RESISTANCE
It is present between a rolling body and the surface on which it rolls. As in the case of sliding
friction, the body and surface are moving relative to each other.
Equitation
In all three cases, the friction equation is the same.
F = µ·N
Symbol and Unit
The symbol µ (the Greek letter mu) is called the coefficient of friction. There is no unit
since it is just a coefficient.
COEFFICIENT OF FRICTION
Every pair of flat surfaces has two different coefficients of friction.
Coefficients of Friction
Material Start Slide
Steel on Steel 0.15 0.09
Steel on Ice 0.03 0.01
Leather on Wood 0.5 0.4
Oak on Oak 0.5 0.3
Rubber on dry Concrete 1.0 0.7
Rubber on wet Concrete 0.7 0.5
Example
A steel body weighing 450 N is resting on a horizontal steel surface. How many newtons of
force are necessary to start the body sliding?
What force is necessary to keep this body sliding at constant speed? w = N = 450 N
F=µ· N
Force to start sliding motion = 0.15 · 450 N = 68 N
Force to keep body sliding = 0.09 · 450 N = 41 N
34
The coefficient of starting friction − µstart

The coefficient of sliding friction − µslide
Coefficients of sliding friction are less than the coefficients of starting friction. This means that the
force needed to start a body sliding is greater than the force needed to keep a body sliding with
constant speed.
When we deal with a body that rolls over a flat surface, we have another coefficient of friction to
consider, the coefficient of rolling friction.
The coefficients of rolling friction ( µroll) are very small. Therefore rolling friction is much smaller
than either starting or sliding friction.
Rubber types on dry concrete 0.02 Roller bearings: 0.001 to 0.003
WORK
General
In ordinary conversation the word ―work‖ refers to almost any kind of physical or mental activity,
but in science and mathematics it has one meaning only.
Work is done when a force produces motion. An engine pulling a train does work, so does
a crane when it raises a load against the pull of the earth.
Similarly, a workman who is employed to carry bricks up a ladder and on to a scaffold platform
also performs work.
Work is said to be done when the point of application of a force moves and is measured by the
product of the force and the distance moved in the direction of the force.
Symbol and Unit
The symbol for Work is typically W, from the english word ―Work―. The Joule (J) is the SI
unit of work.
One Joule is the work done by a force of one Newton acting through a distance of one meter.
Thus: 1 N m = 1 J
Imperial System
In the English system, work is typically measured in Foot−pounds. One foot−pound is equal
to one pound of force applied to an object through the distance of one foot.
One pound is equal to 4.448 Newtons.
Formula a
35
Example 1
If you wish to calculate the work done by a man of mass 65 kg in climbing a ladder 4 m high,
convert weight to Newtons by multiplying 9.81 m/s2 (acceleration of gravity) and multiply this
weight by the height.
W = (65 x 9.8) N · 4 m
W = 2,548 Joules
Example 2
You can see that an object with a force of 600 Newton is moved a distance of 30 meters.
The work is 600 Newton multiplied by 30 meters which is 18.000 Newton meters. This is
18.000 Joule.
POWER
General
When you want to know the ability of a machine to do work in a certain time, you want to know its
power. A strong steam engine will do more work in an hour than a horse.
Power is work over time or more specifically force multiplied by distance over time.
In the figure you can see that the object with a force of 600 Newton is moved a distance of 30
meters in 10 seconds.
The power is 600 Newton multiplied by 30 meters divided by 10 seconds which is 1 800 watts or
1.8 kilowatts.
Symbol and Unit
The symbol for Force is typically P, from the English word ―Power―. The Watt (W) its the SI unit of
power.
One Watt is one Joule per second.
Thus:
Old Unit
You probably know the term horse power. When steam engines were first used their power was
compared to the power of horses because they were used for work which was previously done by
horses.
Formula
Power = P
Work = W
Time = t
P = W/t
Reminder
W=F· d
Figure 30 Power
36
LEVERS
General
A lever is a device used to gain a mechanical advantage.
In its basic form, the lever is a seesaw that has a weight at each end. The weight on one end of
the seesaw tends to rotate the board counter−clockwise while the weight on the other end tends
to rotate the board clockwise. Each weight produces a moment or turning force. The moment of
an object is calculated by multiplying the objects weight by the distance the object is from the
balance point or fulcrum.
A lever is balanced when the algebraic sum of the moments is zero. The symbol for moment is
commonly denoted M.
Example
An object with the weight w=10 N is located two meters to the left of a fulcrum causes a moment
M of negative 20 N m.
An object with the weight w = 10 N located two meters to the right of a fulcrum has a moment of
positive 20 N m.
Since the sum of the moments is zero, the lever is balanced.
Figure 31 Lever I
First−Class Lever
The figure illustrates a practical application of a first−class lever.
The end of a bar with a length of 4 meters is placed under a 100 N weight, 80 the fulcrum is 0,5
meters from the weights center of gravity. This leaves 3.5 meters between the weight and the
point at which the force, or effort is applied.
When the force F is applied, it acts in the direction opposite the weights movement. To calculate
the amount of force F required to lift the weight, you must calculate the moments on each side of
the fulcrum.
This is done using the formula:
Where:
L = length of effort arm
l = length of resistance arm
R = resistance (here: weight of the object)
F = force
37
Although less effort is required to lift a 100−newton weight, a lever does not reduce the amount of
work done.
Figure 32 Lever II
Remember, work is the product of force and distance therefore, when you examine the ratio of
the distances moved on either side of the fulcrum, you notice that the effort arm must move 7 cm
to move the resistance arm 1 cm.
The work done on each side is the same.
0,01 m x 100 N = 0,07 m x 14,28300N=300N
NEWTON’S LAWS
Introduction
The rapid advance in aviation in the first half of the last century can be attributed in large part to a
science of motion which was presented to the world three centuries ago by Sir Isaac Newton, a
British physicist. Newton’s treatise on motion, the ―Philosophize Naturalism Principia
Mathematical― (in short: Principia), published in 1687, showed how all observed motions could
explain on the basis of three laws. The application of these laws have led to great technological
advances in the aerodynamics, structure and power plant of aircraft. It is safe to say that any
future improvements in the performance of aircraft will be based on these laws of motion.
Newton’s First Law
The old magicians trick of pulling a cloth out from under a full table setting is not only a reflection
of the magicians skill but also an affirmation of a natural tendency which dishes and silverware
share with all matter. This natural tendency for objects at rest to remain at rest can be attested to
by any child who ever tried kicking a large rock out of the path.
It is also a well-known fact that once a gun is fired, the command ―stop‖ has no effect on the
bullet. Only the intervention of some object can stop or deflect it from its course. This
38
characteristic of matter to persist in its state of rest or continue in whatever state of motion it
happens to be in is called inertia. This property is the basis of a principle of motion which was first
enunciated by Galileo in the early part of the 17th century and later adopted by Newton as his
first law.
The first law is called the law of inertia. It states:
A body at rest remains at rest and a body in motion continues to move at a constant
velocity unless acted upon by an unbalanced external force.
The importance of the law of inertia is that it tells us what to expect in the absence of forces:
either rest (no motion) or straight line motion at constant speed. A passenger’s uncomfortable
experience of being thrown forward when an aircraft comes to a sudden stop at the terminal is an
example of this principle in action. A more violent example is the collision of a vehicle with a
stationary object. The vehicle is often brought to an abrupt stop.
Unbelted passengers continue to move with the velocity they had just prior to the collision only to
be brought to rest (all too frequently with tragic consequences) by surfaces within the vehicles
(dashboards, windshields, etc.).
Newton’s Second Law
A Learjet accelerates down the runway a distance 1,000 m, takes off and begins its climb at
6,000 ft/min quickly reaching a cruising altitude of 35,000 ft, where it levels off at a speed of 260
knots.
Subsequently, the aircraft may have to perform a variety of maneuvers involving changes in
heading, elevation and speed. Every aspect of the aircraft’s motion is governed by the external
forces acting on its wings, fuselage, control surfaces and power plant. The skilled pilot using his
controls continually adjusts these forces to make the aircraft perform as desired. The interplay
between force and motion is the subject of Newton’s second law. An understanding of this law
not only provides insight into the flight of an aircraft, but allows us to analyze the motion of any
object.
Newton’s second law states:
The rate of change of momentum of a body is proportional to the applied force and takes
place in the direction in which the force acts.
Forcenet = Mass · Acceleration = F = m · a
An increase in velocity with time is measured in the metric system in m/sec. In the Imperial
system it is measured in ft/sec. This is an important relationship when working with the
acceleration of gravity. For example, if a body is allowed to fall freely under the effect of gravity, it
accelerates uniformly at 32.17 ft/s every second it falls. The second law states that a net or
unbalanced force acting on an object equals the mass of the object times the acceleration of that
object.
Inertial Mass
Inertial mass is the mass of an object measured by its resistance to acceleration. To achieve a
given acceleration denoted with a, you need more force for a bigger mass.
According to Newton’s second law, you can use this formula: M= F .
Newton’s Third Law

Newton’s third law is sometimes referred to as the law of action and reaction. This law focuses
on the fact that forces, the pushes and pulls responsible for both the stability of structures as well
as the acceleration of an object, arise from the interaction of two objects.
A push, for example, must involve two objects, the object being pushed and the object doing the
pushing.
Newton’s third law states:
Every action has an equal and opposite reaction.
The thirds law states that no matter what the circumstances, when one object exerts a force on a
second object the second must exert an equal and oppositely directed force on the first.
39
An apple hanging from a tree is pulled by the earth with a force which we call its weight.
Newton’s third law tells us that the apple must pull back on the earth with an exactly equal force.
The weight of the apple is a force on the apple by the earth, directed downward.
The force which the apple exerts back on the earth, is a pull on the earth directed upward.
Another force acting on the apple is the upward pull exerted by the branch. The law of action
and reaction tells us that the apple must be pulling down on the branch with the same
magnitude of force.
People are often confused by this principle because it implies, for instance, that in a tug of war
the winning team pulls no harder than the losing team. Equally enigmatic is how a horse and
wagon manage to move forward if the wagon pulls back on the horse with the same force the
horse pulls forward on the wagon. We can understand the results of the tug of war by realizing
that the motion of the winning team (or losing team) is not determined exclusively by the pull of
the other team, but also the force which the ground generates on the team members feet when
they ―dig in‖.
Recall, it is the net force, the sum of all the acting forces which determine the motion of an
object.
ENERGY
General
The concept of energy is one of the most important concepts in all of physical science. We often
hear of energy sources, alternate energy, shortage of energy, conservation of energy, light
energy, heat energy, electrical energy,
sound energy, etc. So what is the meaning of the word ―energy‖?
Energy is defined as the ―Capacity to do Work‖. This definition is only a partial definition.
However, it has the advantage of immediately relating the concept of energy to the concept of
work. These two ideas are intimately related to each other.
KINETIC ENERGY
Kinetic energy is a quality that a body has after work has been done on this body. Once work has
been done on a body of mass (m) this body has energy. The body can then do work on other
bodies.
Study the following situation.
A body of mass (m) was resting on a table. A player exerted a horizontal force
on this mass through a distance (s). Since the angle between the force and the displacement was
zero degree angle, the work done this body was simply Fs.
At the instant the player removed his cue from the billiard ball we note two facts.
● The body accelerated while the force (F) was acting on the body and the body has acquired
a velocity (v) during this time of acceleration (a).
● The body has moved through a distance (s) in time (t).
Symbol and Unit
The symbol for Kinetic Energy is typically Ek . The Joule (J) is the SI unit of energy.
Formula
Kinetic Energy = Ek Mass = m
Velocity = v
EK = ½ m · v2
POTENTIAL ENERGY
Another equally important situation where an agent easily can do work on a body occurs when
the agent raises a body vertically in a gravitational field, at the surface of the earth. In this case,
the work done on the body again equals the force applied multiplied by the distance the body is
raised.
W = F ·s
W = Weight of Body x Distance Raised
40
here the force F has the same amount as the weight w.

We recall the formula for weight which is a force: w = m x g.
Also since distance is a vertical distance we use the symbol ―h‖ for height. In our discussion we
will assume that the symbol ―h‖ always represents the vertical distance of the body above the
surface of the earth.
Therefore, we write:
W=m· g· h
Again we have a case where an agent did work on a body and the body has acquired ―energy‖.
This type of energy is known as gravitational potential energy.
Symbol and Unit
The symbol for Potential Energy is typically PE. Sometimes, U is used.
The Joule (J) is the SI unit of energy.
Formula
Potential Energy = PE
Mass = m
Gravity = g
Height = h
PE = m · g · h
Summary
If we neglect air resistance (which results in loss of energy to heat), we note that there is a
conservation of kinetic and potential energy of a body moving in a gravitational field.
As a body falls from a height (h) and moves closer to the surface of the earth, its potential
energy decreases and its kinetic energy increases while it is falling.
Therefore, there is an easy way of finding the speed of a falling body during any instant of its
fall.
Example
A body of mass, 10 kg falls to the earth from a height of 300 m above the surface of the earth.
What is the speed of this body just before it touches ground?
The kinetic energy that the body has just before it reaches the ground immediately changes to
sound energy and heat energy on impact. It may also ―squash‖ anybody in its path or make an
indentation in the earth, this is strain energy (energy to deform).
41
Figure 35 Water Wheel
HEAT
General
Heat is a kind of energy. Normally we think of the thermal energy which increases with its
temperature.
In physics, we talk of thermodynamic temperature.
Thermodynamic Temperature is a SI basic quantity.
Symbol and Unit
The symbol for Quantity is T.
The Kelvin (K) is the SI unit of Thermodynamic Temperature.
Thermodynamic
In simple terms, thermodynamic processes start as soon as two bodies with a different
thermodynamic temperature can interact.
In the most common way, this happens when two bodies have contact with each other. As an
example, you can see that a radiator has a different temperature than the surrounding air. This
starts a heat transfer which is called thermodynamic process.
The total amount of energy transferred through heat transfer is conventionally abbreviated as Q.
Since this is energy, its unit is Joule (J).
42
Figure 36 Heat
TOTAL ENERGY
A body of any mass may have various energies:
● Kinetic Energy
● Potential Energy
● Heat Energy
● Electromagnetic Energy.
There are even some more kinds of energy.
Total Energy is just the sum of all these energies in a body.
Example
A cannon ball may have the kinetic energy from the cannon fire and potential energy when the
cannon is standing on a hill.
It may have more energies like heat or magnetism
Figure 37 Cannon
43
EFFICIENCY
General
The efficiency of energy conversion is the ratio between the input into a mechanism and the
useful output of the mechanism.
The useful output may be electric power, mechanical work, or heat.
For example, fuel is burned in an engine. What we want is force to cause a motion. What we do
not want is heat. However, heat will be produced and a radiator is necessary.
Even though the definition includes the notion of usefulness, efficiency is considered a technical
or physical term. Goal or mission oriented terms include effectiveness and efficacy.
Dimension Unit
Generally, energy conversion efficiency is a dimensionless number between 0 and 1.0, or 0%
to 100%. Efficiencies may not exceed 100%, e.g., for a perpetual motion machine.
However, other effectiveness measures that can exceed 1.0 are used for heat pumps and other
devices that move heat rather than convert it. This is causes by the heat caused by friction in the
bearings.
Symbol for Quantity
This is no quantity which can be counted, and so there is no unit.

Formula
The formula is as follows:
Example:
When a cart is pulled, but the bearings of the wheels are not good, heat will be produced
because of the friction. So the power will be converted not only to kinetic energy but also to
some heat energy. By this, we have less kinetic energy.
Figure 38 Efficiency
44
MOMENTUM
Definition of Momentum
Momentum is a vector quantity defined as the product of mass times velocity. Note that velocity
(v) is also a vector quantity.
We write the defining equation as:
Momentum = m · v
Momentum is a very important quantity when we are dealing with collisions, because it is
conserved in all such cases.
CONSERVATION OF MOMENTUM
In a collision, there are always at least two bodies that collide.
We will deal only with collisions of two bodies. We will also limit our discussion to collisions
occurring in one dimension. Such collisions are called ―head−on‖ collisions.
At this time, we need to recall two of newton’s laws. We need Newton’s second law:
F = m·a,
and newton’s third law, which tells us that if two bodies collide, the force that the first body exerts
on the second body is equal in magnitude and opposite in direction to the force that the second
body exerts on the first body. Also recall that the acceleration (a) equals the change in the
velocity divided by the time.
Let us visualize two bodies of masses, M1 and M2 on a one dimensional track. If these two
bodies collide, we have four different velocities to consider. We name these velocities very
carefully.
v1’ = the velocity of body one before the collision. v1‖ = the velocity of body one after the
collision. v2’ = the velocity of body two before the collision. v2‖ = the velocity of body two after the
collision.
By using Newton’s two laws we can derive the following equation.
The equation tells us that the total momentum before the collision is equal to the total momentum
after the collision. Sometimes we say simply that ―Momentum is Conserved‖.
m1 ·v1’ + m2· v2’ = m1· v1’ + m2 ·v2‖
The simplest example of the conservation of momentum is in recoil problems.
Example
A boy and a man are both on ice skates on a pond.
The mass of the boy is 20 kg and the mass of the man is 80 kg. They push on each other and
move in the opposite directions.
If the recoil velocity of the boy is 80 m/s, what is the recoil of the man?
First we note that both the man and boy are at rest before the collision occurs.
The negative sign indicates that the man recoils in the opposite direction from the boy.
IMPULSE
Collision Problems
Whenever two bodies collide, momentum is always conserved. This is simply the result of
applying Newton’s second and third laws as we have done in the preceding discussion.
Sometimes kinetic energy is also conserved in a collision. This happens when the bodies are so
hard that there is very little deformation of the bodies in the actual collision process. Billiard balls
45
are a good example. These collisions are known as elastic collisions. We will derive a formula for
determining the velocities of the bodies after the collision has occurred.
Another type of collision that we will discuss is the perfectly inelastic collision. In this type of
collision, the bodies are deformed so much that they actually stick together after the collision. An
example would be the collision of two masses of putty. We will also do some problems for this
type of collision.
Inelastic Collisions
We use the conservation of momentum for dealing with this type of collision. As we have said, the
colliding bodies stick together after impact.
Therefore, the equation is simply:
m1· v1’ + m2· v2’ = (m1 + m2) · v‖
Note that we use the symbol v‖ for the common velocity of the two bodies (which are now one
body) after the collision.
It is important to include the signs of the velocities of the bodies in setting up momentum
equations. As usual, we use a positive sign for east and a negative sign for west, a positive sign
for north and a negative sign for south.
Example
A truck with a mass of 1550 kg is moving east at 60 m/s. A car with a mass of 1250 kg is
travelling west at 90 m/s the vehicles collide and stick together after impact.
What is the velocity of the combined mass after the collision has occurred?
m1· v1’ + m2 ·v2’ = (m1 + m2) · v‖
1550 kg · 60 m/s + 1250 kg · −90 m/s = (1550 kg + 1250 kg )· v‖
−19500 kgm/s = 2800 kg · v‖
v‖ = −6.96 m/s
Since the calculated velocity has a negative sign, we conclude that the combined mass is
travelling west after the impact occurred.
Our answer is that the wreckage starts to move west with a speed of 6.96m/sec. Sometimes the
principle of conservation of momentum in the case of an inelastic collision can be used by the
police to determine the speed of a vehicle engaged in a head−on collision.
Figure 39 Inelastic
Collision
46
Elastic Collisions
Elastic collisions are collisions that occur between bodies that deform very little in the collision.
Therefore we assume that no energy is lost. An example of such a collision is the collision
between pool balls.
In elastic collisions, both kinetic energy and momentum are conserved. In an ordinary elastic
collision problem, we know the masses and the velocities of two bodies that will collide. We want
to predict, by mathematical calculation, the velocities the bodies will have after the collision has
occurred, the two unknowns.
If we write the two conservation equations, we have two equations in these two unknowns. It is
possible to solve these two equations for these two unknowns. However, one of the conservation
equations, the energy equation, is a ―second order‖ equation. A ―second order‖ equation contains
the squares of the unknowns. This makes the solution more difficult. Instead, we will use an
algebraic trick! The two conservation equations can be solved together producing a third
equation. This third equation and the momentum conservation equation provide the two first order
equations that we will use in solving elastic collision problems.
The following two equations have been obtained algebraically and must be used for carrying out
elastic collision calculations.
(1) m1· v1’ + m2 ·v2’ = m1· v1’’ + m2· v2‖
(2) v1’ − v2’ = v2‖ − v1‖
Example
A billiard ball of mass 2 kg is moving east at 3 m/s and undergoes an elastic collision with another
billiard ball of mass 3 kg moving west at 4 m/s. Find the velocities of the two balls after the
collision.
m1 = 2; v1’ = 3 (east) m2 = 3; v2’ = −4 (west)
Substitute in equation (1):
2 · 3 + 3 · −4 = 2 ·v1’ + 3 ·v2‖
(3)−6= 2 ·v1’ + 3· v2‖
Substitute in equation (2):
3 − (−4) = v2‖ − v1‖
(4) 7 = v2‖ − v1‖
Rewrite equations (3) and (4) putting the unknowns in the left members and in order.
(3) 2 v1’ + 3 v2‖ = −6
(4) −v1‖ + v2‖ = 7
We now have two equations and two unknowns. There are several methods of solving such a
system of equations. We will use the method of addition. In this method we multiply either or
both of the equations by constants to make the coefficient of one of the unknowns in the one
equation a positive number and to make the coefficient of this same unknown in the other
equation a negative number of the same magnitude. We then add the two equations to
eliminate one of the unknowns. We then solve for the other unknown by substituting in either
equation.
Multiply (4) by the number 2
Add (3) and (5)
Substitute this value back into (4)
47
We note that we interpret a positive sign for the velocity as motion east and negative sign as
motion west.
Our final result is that the 2 kg ball is moving west with a speed of 5.4 m/s after the collision
and the 3 kg ball is moving east with a speed of 1.6 m/s after the collision.
GYROSCOPIC PRINCIPLES
General
Gyroscopes or gyros in short are fascinating to study and a great deal of material is
available on them.
For the most part, we will be connected with only two of the properties of the spinning gyros.
Gyros are used to detect turns around the x, y or z axis of an aircraft.
Rigidity in Space
The first is the tendency of a spinning gyro to remain fixed in space if it is not acted upon by
outside forces such as bearing friction. This is the property of rigidity.
Rigidity is used in gyros to show the direction (Horizontal Situation Indicator or HSI) and
attitude (Attitude Director Indicator or ADI) of an aircraft.
Figure 41 Rigidity in Space
48
Precession
The other property of a spinning gyro that concerns us is its right angle obstinacy. It never
goes in the direction that you push it, but off to one side. The diagram below illustrates this
obstinate characteristics. The rules for anticipating the actual direction of motion from a given
applied force are shown below.
Whichever way you apply the force to the axis of a gyro, it will move in a direction 90˚ (in the
direction of rotation) to the force. The speed at which it moves is
proportional to the force applied. This action is called precession.
The force of precession is used in rate gyros, such as those in a turn and slip indicator, where
the speed of turn is measured by the force that the processing gyro exerts on a spring.
Figure 42 Gyro Precession

SPECIFIC GRAVITY AND DENSITY
Density
Equal volumes of different substances vary considerably in their mass.
For instance aircraft are made chiefly from aluminum alloys which, volume for volume, have a
mass half that of steel, but are just as strong. The lightness or heaviness of a material is
referred to as its density.
The density of a substance is its weight per unit volume. The density of solids and liquids
varies with temperature. However, the density of a gas varies with temperature and pressure.
To find the density of a substance, divide the weight (mass) of the substance by its volume.
Symbol and Unit
The symbol for quantity is r (Greek small rho).
The kilogram per cubic meter (kg/m2) is the SI unit of density.
49
Formula
Density = r
Mass = m
Volume = V
Other algebraic forms of this same equation are:
Example
The liquid which fills a certain container has the mass of 326,4 t and weighs 3.2 MN (Mega
newton).
The container is 4 m long, 3 m wide and 2 m deep. Therefore its volume is 24 cubic meters.
Based on this the liquids density is 13 600 kg/m3
3264OO hg
13 600 kg/m3 =
24 m3
Because the density of solids and liquids vary with temperature, a standard temperature of 4
˚C is used when measuring the density of each. Although temperature changes do not change
the volume of a substance through thermal expansion or contraction. This changes a
substances weight per unit volume.
When measuring the density of a gas, temperature and pressure must be considered.
Standard conditions for the measurement of gas density is established as 0 ˚C and a pressure
of 1013 hPa (29.92 inches of mercury column) which is the average pressure of the
atmosphere at sea level.
Specific Gravity
It is often necessary to compare the density of one substance with that of another. For this
reason, a standard is needed from which all other materials can be compared. The standard
when comparing the densities of all liquids and\solids is water at 4 ˚C.
The standard for gases is air.
In physics the word ―specific‖ refers to a ratio. Therefore, specific gravity is calculated by
comparing the weight of a definite volume of substance with the weight of an equal volume of
water. This is why ―Specific Gravity― is also called ―Relative Density―.
Symbol
The symbol for quantity is RD.
Formula
The following formulas are used to find specific gravity (sp. gr.) of liquids and solids.
The same formulas are used to find the density of gases by substituting air for water. Specific
gravity is not expressed in units, but as a pure number.
Hydrometer
A device called a hydrometer is used to measure the specific gravity of liquids. This device has
a tubular shaped glass float contained in a larger glass tube.
50
The float is weighted and has a vertically graduated scale. The scale is read at the surface of
the liquid in which the float is immersed. A reading of 1000 is shown when the float is
immersed in pure water.
When filled with a liquid having a density greater than pure water, the float rises and indicates
a greater specific gravity. For liquids of lesser density, the float sinks below 1000.
The specific gravity of a liquid is

measured with a43
Figure hydrometer
Hydrometer
Liquids kg/m3 slug/ft3
Water 1000 1.940

Sea Water 1030 2.00
Benzene 879 1.71
Alcohol 789 1.53
Gasoline 680 1.32
Kerosene 800 1.55
Sulfuric Acid 1831 3.55
Mercury 13600 26.3
51
DENSITY AND SPECIFIC WEIGHT TABLES

Density
The table shows some examples for the density r of various materials
Metals kg/m3 slug/ft3

Aluminum 2700 5.25
Cast Iron 7200 14.0
Copper 8890 17.3
Gold 19300 37.5
Lead 11340 22.0
Nickel 8850 17.2
Silver 10500 20.4
Steel 7800 15.1
Tungsten 19000 37.0
Zinc 7140 13.9
Brass 8700 16.9
Non−Metals kg/m3 slug/ft3

Ice (32°F, 0°C) 922 1.79
Concrete 2300 4.48
Glass 2,600 4.97
Granite 2700 5.25
Woods kg/m3 slug/ft3
Balsa 130 0.25
Pine 480 0.93
Maple 640 1.24
Oak 720 1.4
Ebony 1200 2.33
52
Specific Weight
The table shows some examples for the specific weight g of various materials
Weight Densities at 20°C/ 68 F
Liquids kN/m3 lbf/ft3
Water 9,807 62.4

Ocean Water 10,100 64.4
Benzene 8,620 54.9
Carbon Tetrachloride 15,630 99.5
Ethyl Alcohol 7,740 49.3
Gasoline 6,670 42.5
Kerosene 7,850 49.9
Lubricating Oil 8,830 56.2
Methyl Alcohol 7,770 49.4
Sulfuric Acid 100% 17,960 114.3
Turpentine 8,560 54.5
Weight Densities at 20°C / 68 F
Nonmetallic Solids ˚
kN/m3 lbf/ft3
Ice 9,040 57.5

Concrete 22,600 144
Earth, packed 14,700 94
Glass 25,500 160
Granite 26,500 169
Woods kN/m3 lbf/ft3
Balsa 1,270 8
Pine 4,700 30
Maple 6,300 40
Oak 7,100 45
Solid Metals kN/m3 lbf/ft3
Aluminum 26,500 169

Cast Iron 70,600 449
Copper 87,200 555
Gold 189,300 1,205
Lead 111,200 708
Magnesium 17,100 109
Nickel 86,800 553
Silver 103,000 656
Tungsten 186,000 1,190
Zinc 70,000 446
˚
53
PRESSURE
General
Pressure is defined as the force divided by the area on which the force acts. For example, the
pressure exerted on the ground by a body depends on the area of the body in contact with the
ground. A person wearing ice skates will exert a far greater pressure than a person wearing
shoes.
Formula
The equation defining pressure is:
Example
On a day when the atmosphere pressure is 1020 hPa, what is the force acting on a desk top
having an area of 2,5 m2 ?
Force = Pressure × Area = 1020 hPa x 2,5 m2
Force = 102 kPa x 2,5 m2
F = 102 kN/m2 x 2,5 m2
F = 102 kN x2,5
F = 255 kN
The molecules making up a gas are in ceaseless motion. They collide and rebound from any solid
surface which they encounter. These collisions result in a net push or force on the surface. As we
have said, this force, divided by the area of the surface over which it is exerted, is called
pressure.
Atmospheric Pressure
On our earth, we live under a blanket of air. The density of air decreases with altitude.
At sea level, the average atmospheric pressure is 101,3 kPa, commonly written as 1013 hPa.
This is 14.7 lbf/in2. Various types of barometers are used to measure atmospheric pressure.
The mercury barometer is a narrow vertical glass tube which is inverted in a dish of mercury.
The small space above the mercury column is a perfect vacuum. As the air molecules bombard
the surface of the mercury in the dish, they balance the mercury in the column since there are
no bombarding molecules above the mercury in the column. The height of the mercury column
varies slightly from day to day as the atmospheric pressure changes.
At standard pressure (14.7 lbf/in2) the mercury column is 760 mm high. In the English system
the height of the mercury column is 29.92 inches. Sometimes we use the height of mercury
(Hg) column as a unit for stating pressure.
We can say:
1 Atmosphere = 1013 hPa = 14.7 lbf = 760 mmHg = 29.92 inHg
NOTE: Since mercury expands with an increase in ambient temperature, the barometer must
be corrected to that which it would read at the accepted value of room temperature 20 ˚C or 68
˚F
Absolute & Gauge Pressure
All of the pressure measuring instruments which the aircraft mechanic is likely to use are
designed to register the extent to which the pressure being measured differs from the ambient
pressure. The term ―ambient pressure‖ refers to the pressure in the area immediately
surrounding the object under study.
For example, a tire gauge registering 32.0 psi is telling us that the pressure inside the tyre is
32.0 psi greater than the pressure outside the tire. On a day when the atmospheric pressure is
54
1006 hPa (14.6 psi), the actual pressure the gas is exerting on the inner walls of the tire is 46.6
lbf/in2 (32.0 + 14.6).
The actual pressure the gas is exerting on the walls of its container is called the absolute
pressure. The general relation which connects gauge pressure, absolute pressure and
atmospheric pressure is:
Pabs = Pg + Patm
The zero on the absolute pressure scale is the pressure exerted by a perfect vacuum.
Let assume that the atmospheric pressure on a certain day is 15 psi (15 lbf/in2). The table
below gives the gauge pressure and the absolute pressure for several different examples.
The equation Pabs = Pg + Patm is satisfied in each entry.
Absolute Pressure Gauge Pressure

lbf/in2 (psi) lbf/in2 (psi)
Inside a tire 49 34
Pressure cooker 35 20
Outside air 15 0
Cabin pressure of an a/c 11 −4
Perfect vacuum 0 −15
STATIC, DYNAMIC AND TOTAL PRESSURE

General
Gravity, applied forces and atmospheric pressure are static factors that apply equally to fluids at
rest or in motion, while inertia and friction are dynamic factors that apply only to fluids in motion.
Static Pressure
The mathematical sum of gravity, applied force, and atmospheric pressure is the static pressure
obtained at any one point in a fluid at any given time.
Static pressure exists in addition to any dynamic factors that may also be present at the same
time.
Dynamic Pressure
Remember, Pascal’s Law states that a pressure set up in a fluid acts equally in all directions
and at right angles to the containing surfaces. This covers the situation only for fluids at rest or
practically at rest. It is true only for the factors making up static head.
Obviously, when velocity becomes a factor it must have a direction, and as previously
explained, the force related to the velocity must also have a direction, so that Pascal’s law
alone does not apply to the dynamic factors of fluid power.
Total Pressure
The dynamic factors of inertia and friction are related to the static factors. Velocity head and
friction head are obtained at the expense of static head.
However, a portion of the velocity head can always be reconverted to static head.
Force, which can be produced by pressure or head when dealing with fluids, is necessary to
start a body moving if it is at rest, and is present in some form when the motion of the body is
arrested; therefore, whenever a fluid is given velocity, some part of its original static head is
used to impart this velocity, which then exists as velocity head.
55
Example 1
In the figure below, you see the static air pressure which lasts on the roof of a house. This is
caused by the gravity which pulls on the air which is directly above the house.
Since there is also air inside the house, there is a counter pressure.
If there was a vacuum inside the house, the column of air would bend the roof downwards.
The mass of the air column is about 10 000 kg on one square meter.
Example 2
Imagine a hermit crab housing in a snail shell.
The static pressure on his house is caused by the water column above.
Since there is also water inside the shell and inside the crab’s body, there is a counter
pressure.
When animals are pulled out of the deep sea, they explode because the static pressure is
decreased rapidly around them.
Figure 44 Static Pressure
EFFECTS OF COMPRESSIBILITY ON FLUIDS

General
The term compressibility is used when an increase in pressure will result in a decrease of
volume of the affected material.
In fluids, however, the compressibility is extremely low. Thus, an increase of pressure in fluids will
have nearly no change in volume.
Pressure in Fluids
There are two ways to increase the pressure of fluids:
● A kind of vat.
Gravity pulls all molecules of the fluid down. The lower the portion which is looked at, the higher
is the pressure. Example: an ocean is a big vat.
● A closed container and a force which tries to decrease the volume of that container.
Example: a cylinder and an appropriate piston within.
Compressibility
For each fluid, there is a content factor to calculate the volume change caused by pressure. This
is the compressibility.
Symbol and Unit
The unit is m2/N or
1/Pa.
56
Formula
With the help of the compressibility, the change of volume caused by a change of pressure is
calculated like this:
The negative value is due to the decrease of volume when the pressure increases.
Example 1
A cylinder is filled with fluid. When a piston is moved downwards with the force F, the piston
will move the distance d.
When you know the diameter of the cylinder, you can calculate the change in volume. This
Example 2
When you know the compressibility of the fluid, the total volume and the change in pressure,
he distance
d.
Figure 45 Compression of Fluids
VISCOSITY
General
The factor which most affects the behavior of a fluid in motion is the viscosity of the fluid. This is
the fluid’s own resistance to flow and is due to internal friction within the fluid. In a liquid this
internal friction is caused by intermolecular
attraction and in a gas it is caused by the interchange of molecules between the different layers.
The viscosity of the fluid will be influenced by the temperature, normally the hotter the liquid
becomes, the lower the viscosity. This is called a positive coefficient of viscosity.
A few materials have a negative coefficient of viscosity and increase their viscosity with
temperature.
Fluid Flow
57
The fluid can flow in different ways depending on the shape of the duct in which it is contained
and on the viscosity of the fluid.
If the flow is disorderly then the speed and direction of the particles passing a particular point
will be constantly changing, this is known as Turbulent Flow.
If the flow is steady then all the particles passing a particular point will have the same direction
and speed. This is known as Steady Flow.
Laminar Flow
This is an example of a type of steady flow where the particles of a particular streamline all
travel at the same speed but each adjacent streamline is travelling at a different speed. This is
due to the viscosity of the fluid. For example, if a fluid is flowing next to the skin of an aircraft
then the layer of air next to the skin will not be moving at all relative to the skin. The next layer
will be moving at a low velocity, the next layer slightly faster and so on until the full, free stream
velocity is reached. This arrangement is normally the most desirable on an aircraft because it
causes the least air resistance (drag) on the aircraft. For this reason, the aircraft is made with a
smooth shape to encourage laminar flow, this smoothing of the shape is called streamlining.
In the diagrams below we can see examples of laminar flow inside a duct. The effect of the
fluid’s viscosity can be seen as the layer immediately adjacent to the wall of the duct is not
moving at all and each subsequent layer is moving a little faster. The more viscous the fluid
then the greater this effect would be.
Figure 46 Longitudinal Cut of Fluid Flow Showing

Laminar Flow in a Circular Duct
FLUID RESISTANCE AND EFFECTS OF STRAMLINING

General
When a car is on the highway, its speed is not only limited by speed limits. The maximum speed
is reached when the engine performs maximum power, but the forces of friction and drag have
the same value. Thus, further acceleration is not possible.
In this case, drag is the air resistance.
FLUID RESISTANCE
On a ship or a submarine, speed is also limited by the drag. In this case, drag is
the fluid resistance.
In fluids, the following factors are important for the calculation of fluid resistance:
● size of the object
58
● form of the object

● density of the fluid
Additionally, the drag increases with the square of velocity.
Symbol and Unit
Fluid resistance is a kind of force. The symbol for quantity is Fd. The newton (N) is the
SI unit of force.
Formula
To calculate the force of drag Fd you need the following factors:
● size of the object (reference area) A
● form of the object which results in a coefficient of drag Cd
This is a dimensionless parameter and thus it has no unit.
● density of the fluid
● speed of fluid or object in fluid v
With everything in a correct relation the formula is as follows:
STREAMLINING
Normally, a sports car is streamlined and an old van is not. The reason is, that a sports car is
bought by people who want to drive fast. For a given engine power, a low drag is a means to
increase the maximum speed.
The drag depends on the size and the shape of the car.
Thus, when the size of an object is given, the drag can be reduced by streamlining its hull.
The same is true for ships and submarines and any other objects in fluids. The coefficient of drag
Cd is a result of the shape of the object.
A kind of wall has a great resistance. The resistance is not only caused by the
front, but also by the rear. This is because the form of the rear determines the strength of
turbulences.
Examples
In the figure below, you see various objects and their drag coefficient.
Figure 47 Drag Coefficient
59
BERNOULLI’S PRINCIPLE
General
The Swiss mathematician and physicist Daniel Bernoulli developed a principle that explains the
relationship between potential and kinetic energy in a fluid. As discussed earlier, all matter
contains potential energy and/or kinetic energy. In
a fluid, the potential energy is that caused by the pressure of the fluid, while the kinetic energy
is that caused by the fluids movement.
Although you cannot create or destroy energy, it is possible to exchange potential energy for
kinetic energy or vice versa.
Figure 48 Bernoulli’s Principle

Bernoulli’s principle states that when energy is neither added to nor taken from a fluid in motion,
the potential energy, or pressure decreases when the kinetic energy or velocity increases.
VENTURI
A venture tube is a specially shaped tube that is narrower in the middle than at the ends.
As fluid enters the tube, it is travelling at a known velocity and pressure. When fluid enters the
restriction, it must speed up, or increase its kinetic energy.
However, when the kinetic energy increases, the potential energy decreases.
Then as the fluid continues through the tube, both velocity and pressure return to their original
values.
A venture tube is a tube constructed in such a way that the cross−sectional area of the tube
changes from a larger area to a smaller area and finally back to the same larger area. As a fluid
flows through this tube the velocity changes from a lower velocity to a higher velocity and finally
back to the same velocity. We note that, if the rate (volume per second) of fluid flow is to remain
constant, the fluid must flow faster when it is flowing through the smaller area.
The height of the fluid column in the vertical tubes at the three places shown in the figure below,
is an indication of the fluid pressure. As we expect from Bernoulli’s Principle, the pressure is
greater where the velocity is lower and vice versa. Venturi tubes in different shapes and sizes are
often used in aircraft systems.
If we consider the types of energy involved in the flowing fluid, we find that there are three types
− potential (gravitational), pressure and kinetic energies. Consider only the two positions in the
venture, the wide part (1) and the narrow section (2), and consider the conservation of energy
principle.
60
Potential Energy at 1 Potential Energy at 2

+ +
Pressure energy at 1 = Pressure Energy at 2
+ +
Kinetic Energy at 1 Kinetic Energy at 2
The above is assumed since the total energy in the fluid cannot change, only transferred from
one form to another. This is the basis for Bernoulli’s Formula.
Since the Ventura in this case is horizontal, there is no change in potential energy, and so the
potential energies can be cancelled from the formula;
Pressure energy at 1 Pressure Energy at 2
+ = +
Kinetic Energy at 1 Kinetic Energy at 2
Figure 49 Venturi Tube
61
SUB-MODULE 03 - THERMODYNAMICS
Temperature thermometers and temperature scales: Celsius,
Fahrenheit and Kelvin; Heat definition;

Objectives:
(c) The applicant should be familiar with the basic
(d) The applicant should be able to give a simple
words and examples.
62
TEMPERATURE
General
Our common notion of hot and cold has its precise expression in the concept of temperature. As
objects are heated their molecules move faster. In a solid the molecules vibrate more rapidly. In
liquids and gases the molecules move all over in the container at a faster rate of speed. These
variations in speed of the molecules cause objects to expand when they are heated.
This expansion can be used to construct instruments called thermometers. The ordinary mercury
thermometer uses the expansion of a volume of mercury contained in a bulb to indicate
temperature.
Temperature is a SI basic quantity.
Symbol and Unit
The symbol for Temperature is T.
The Kelvin (K) is the SI unit of temperature.
TEMPERATURE SCALES
Celsius and Fahrenheit
A number of temperature scales are currently in use.
The metric scale is the Celsius or centigrade scale. On this scale the freezing point of water is
zero and the boiling point is 100 ˚C.
The Fahrenheit scale is used in the imperial system. On this scale the freezing point of water is
32 ˚F and its boiling point is 212 ˚F.
Kelvin and Rankin
Two other temperature scales are used by engineering and experimental scientists. In both of
these scales the zero of the scale is placed at absolute zero, the coldest possible temperature.
These scales are the metric Kelvin scale and the English Rankin scale.
Absolute Zero
In theory, if we cool any substance enough, we can cause all molecular motion to cease. We
call this lowest possible temperature ―absolute zero‖. Ordinary gases like air would be rock
solid at this temperature. Low temperature physicists have never been able to reach this
extremely low temperature in their laboratories. However, they have come close to a fraction
of a centigrade degree. Absolute zero is a limiting temperature which can never be reached.
Because to reach it we would need a cooling agent which is colder as zero Kelvin, or
―absolute zero―.
Conversion from Celsius to Fahrenheit
There are formulas that enable us to change from the Celsius reading to a Fahrenheit reading
and vice versa.
These formulas are:
C = 5 (F — 32)
9
and in reverse
F = 9 + 32
5
Conversion from Celsius to Kelvin
There are also formulas that change from a Celsius reading to a Kelvin reading and from a
Fahrenheit reading to a Rankin reading.
63
These formulas are very important to us at this time since we will have to use absolute
temperatures in the gas laws.
These formulas are:
K = °C + 273
and in reverse
R = °F + 460
NOTE: Kelvin has no ˚ sign in front of the K. The accurate conversion factor for ˚C to K is +
273.15.
Example
20˚C = 293,15 K
Conversion from Fahrenheit to Rankin
The conversion factor for ˚F to R is: plus 460.
Example
32˚F = 492 R
Boiling point of Freezing point of Absolute zero

Unit Water Water
Celsius 100 deg 0 deg −273 deg

Kelvin 373 273 0
Fahrenheit 212 deg 32 deg −460 deg
Rankin 672 deg 492 deg 0 deg
HEAT DEFINITION
General
We recall that temperature is a measure of the average kinetic energy, and therefore the average
velocity, of the molecules of the substance whose temperature is being measured.
Energy
Heat is a measure of the total energy of molecular motion. The more molecules that are moving,
the greater is the heat energy.
Example 1
Let us compare a teaspoon of water at 90 ˚C with a cup of water at 50 ˚C. The molecules of water
in the teaspoon are moving faster than the molecules of water in the cup. However, since we
have so many more molecules in the cup, the heat energy in the cup is greater than the heat
energy in the teaspoon.
If the teaspoon of water is placed on a large block of ice and the cup of water also placed on the
this block of ice, the cup of water at 50 ˚C would melt more ice than the teaspoon of water at 90
˚C.
Example 2
In the figure below, you see some objects. They have all the same temperature.
But when they have a different mass, then the objects with the bigger mass have more heat.
Symbol and Unit
The symbol for Heat is Q.
The Joule (J) is the SI unit of heat.
64
Reminder
One Joule is the work done by a force of one Newton acting through a distance of one meter.
Thus: 1 Nm = 1 J
Other Units
There are older units for measuring heat energy.
The units are the Btu (British Thermal unit) and the metric units are Calorie (C). 1 British
Thermal unit (Btu) = the amount of heat needed to raise the temperature of 1lb of water 1 ˚F
1 Calorie = the amount of heat needed to raise the temperature of 1 kilogram of water 1 ˚C.
(Note: 1 Calorie = 1 Kcal = 4186 J, 1 Btu = 0,252 Cal)
1 calorie = the amount of heat needed to raise the temperature of 1 gram of water 1 ˚C 1
Celsius Heat Unit (CHU) = the amount of heat needed to raise the temperature of 1lb of water
1 ˚C
NOTE: The CHU is a mix of English and Metric units and is rarely used
When we talk about the heat content of fuel (which must be burnt to be released) commonly
called the heat of combustion, we talk about Calories per lb of fuel, or Btu per lb of fuel, or
Joules per kg of fuel.
Since 1 Btu = 252 calories and
1 cal = 4.186 Joules,
there are 1055 joules in 1 Btu.
Since 1 lb = 0.454 kg,
1 Btu/lb = 480 J/kg.
We note that the calorie is the famous dietary Calorie. The body stores excess food as fat and
we measure the Calories in a certain foodstuff by burning these foodstuffs and measuring the
heat produced.
In the solution to heat problems, we will limit our discussion to the English system, since this is
the system that is most often used in our society.
INTRODUCTION
Unit Systems
The system of measurement is based mainly on the International System of Units, usually
abbreviated SI (french: System International).
However, aircraft maintenance data expressed in imperial units (English system) and US units
are still used and will remain in use for many years.
Therefore the aircraft mechanic need to know both the SI and imperial systems together with
some US variations of the imperial system, and the knowledge of conversion.
BASE UNITS
General
Seven base units are used in the SI system. The seven base (or
primary) SI units are:
65
Supplementary Units
Two supplementary units relate t quantities of angle. One is for plane angles (the region cut out in
a plane by two straight lines diverging from a point), and the other for solid angles (the region cut
out in space by an arbitrary cone):
The Symbol for Quantity may be different depending on the language. For example, the
Symbol for Voltage is V, whereas in German the symbol for ―Spannung― is U.
There are also minor differences between British English and American English. For
example, for length the Americans write ―meter― , whereas the British write ―metre―.
DERIVED UNITS
Introduction
Derived units are always made up from two or more other units which may be base units,
supplementary units or other derived units. Some derived units such as the joule, the watt and
the newton are named after eminent scientists.
Others have complex names which are derived from the units comprising them, such as meter
per second (a combination of two base units) and radians per
second (a combination of a supplementary unit and a base unit).
Derived Units
Derived Units with Complex Names
Name of Quantity Derived Unit Symbol for Unit

Frequency hertz Hz
Force newton N
Pressure pascal Pa
Work joule J
Power watt W
Electric Charge coulomb C
Voltage (Electromotive volt V
Force)
Electrical Capacitance farad F
66
Electrical Resistance ohm fi

Electrical Conductance siemens S
Electrical Inductance henry H
Name of Quantity Derived Unit Symbol for Unit

Heat Capacity joule per kelvin J/K
Apparent Power volt ampere VA
Velocity, Speed meter per second m/s
Torque newton meter Nm
Density kilogram per cubic kg/m3
meter
SI SYMBOLS AND PREFIXES

General
The plural of a symbol is identical to its singular form, as with 1 m and 153 m.
Symbols for derived units with complex names are combinations of the constituent unit
symbols.
Products
The product of two or more unit symbols may be indicated by a half-high dot, or where there is no
risk of confusion with another unit symbol, the dot may be omitted and a space is used.
Thus N·m or N m is the symbol for newton meter.
Divisions
The division of one unit by another in a complex unit is indicated by a negative index, an oblique
stroke(/), or a horizontal line.
For example, a kilogram per cubic meter (the unit for desnity) is expressed as
● kg m-3,
● kg/m3,or
● \
Multiples and Submultiples

Factors of 10 are always used as multiples and submultiples of SI units.
The meter for example, is useful for measuring objects such as the size of a hangar, but many
zeros would be required to express the maximum range of a jet airliner in meters.
Similarly it would be cumbersome to express small measurements, such as a conact breaker
gap, as a decimal fraction of a meter.
Prefix
Multiples and submultiples of SI units are formed by attaching a prefix to the name of the unit.
The symbol and the multiplication factor of the prefix listed in the table.
Generally, it is preferable to use the prefixes that advance or decline by factors of 10 3. Thus
the use of hecto, deca, deci and, to a lesser extent, centi, are not encouraged. The most
commonly used prefixes are kilo, mega, milli and micro.
Prefix symbols should be written or printed without spacing between the prefix symbol and the
unit symbol, as in mm and kW.
67
Compound prefixes, such as milli−micro should not be used.

In general only one prefix should be used in forming the symbol for a unit.
Metric Prefixes
Measurement of UNITS IN ICAO TABLE UNITS IN BLUE TABLE

Distance used in navigation
position re- porting etc. — NAUTICAL MILES and NAUTICAL MILES and
generally excess of 2 to 3 TENTHS TENTHS
nautical miles
Relatively short
distances such as METERS METERS
runway lengths
Altitudes, elevations and
METERS feet
heights
Horizontal speed including
KNOTS KNOTS
wind speed
Vertical speed METERS PER SECOND feet per minute
Wind direction for landing
DEGREES MAGNETIC DEGREES MAGNETIC
and taking off
Wind direction except for
DEGREES TRUE DEGREES TRUE
landing and taking off
Visibility including runway
KILOMETERS or METERS KILOMETERS or METERS
visual range
Altimeter setting MILLIBARS MILLIBARS
DEGREES CELSIUS DEGREES CELSIUS
Temperature
(CENTIGRADE) (CENTIGRADE)
METRIC TONS METRIC TONS
Weight (see Note 2 below) (TONNES) (TONNES) or
KILOGRAMMES KILOGRAMMES
HOURS and MINUTES, THE HOURS and MINUTES, THE
Time DAY OF 24 HOURS DAY OF 24 HOURS
BEGINNING AT MIDNIGHT BEGINNING AT MIDNIGHT
ICAO SPECIFIED UNITS FOR A/C COMMUNICATIONS

General
68
The International Civil Aviation Organization (ICAO) in its role of promoting international
standards and recommended practices has published two alternative tables of units of
measurement for use in air to ground
communication.
These are:
● the ICAO Table and
● the Blue Table.
They differ only in the units specified for altitudes and vertical speed.
Most English−speaking countries have adopted the Blue Table, but some of these countries vary
from it for some units.
Note 1: Wherever units are common to both tables they appear in the Blue Table printed in
capitals. Note 2: ICAO uses the term ’weight’ to denote ’mass’.
General
As already mentioned, the majority of the countries in Europe and most of the countries in the
world are using the SI units to define the basic units and their derived units.
The remaining countries e.g. Great Britain and the USA are using an older system called the
imperial system. The imperial system uses units which are historically grown and developed over
centuries (e.g. feet, inches, yards, pounds and gallons). It is still used in aviation until today.
69
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Lot 43A, Quang Minh

Module 01 Syllabus as outlined in PART-66

CERTIFICATION CATEGORY LEVEL

Sub-Module 02.1 – Statics

Simple theory of vibration, harmonics and resonance;

(b) Momentum, conservation of momentum; 1

CONSERVATION OF MOMENTUM ............................................................................................... 45

LEVEL 1: A familiarization with the principal

PROTONS, ELECTRONS AND NEUTRONS

STRUCTURE OF ATOMS AND FREE ELECTRONS

Figure 1: Atomic Shell and Free Electrons

THE ELECTRONIC STRUCTURE OF ATOMS

THE CHEMICAL ELEMENTS

Figure 3 Table of Elements

Figure 4 Physical States

CHANGES BETWEEN STATES

Figure 5: Boiling and Condensing

Figure 6: Melting and Freezing

UNIFORM MOTION IN A STRAIGHT LINE

seconds, we cover 100 meters,

MOTION UNDER CONSTANT ACCELERATION

The standard gravity is defined as follows:

Converted into the imperial system, the gravity is

However, this value is only correct on the earth’s surface.

Figure 8 Free Fall

For circular motion,

This force is called the centripetal force.

Figure 9 Hammer Throwing

Figure 10 Simple Pendulum

SIMPLE THEORY OF VIBRATION, HARMONICS AND RESONANCE

MECHANICAL ADVANTAGE, VELOCITY RATIO AND EFFICIENCY

A mechanical advantage of 4 indicates that for every 1 newton of force applied, 4

As we usually express efficiency in percent, we multiply the result of the

Figure 12 Pulleys and Mechanical

LEVEL 1: A familiarization with the principal

Figure 14 Addition of Vectors (Velocity)

Figure 15 Addition of Vectors (Force)

STRESS, ELASTICITY AND STRAIN

Figure 16 Center of Gravity

Five Kinds of Stress

Figure 18 Rubber Band

Figure 19 Torque Wrench

Another example is the forces applied to a car steering wheel.

Figure 21 Control Wheel

NATURE AND PROPERTIES OF MATTER

(density = Mass ÷ Volume).

Relationship of Force, Pressure & Head

Figure 23 Static Pressure

The pressure produced in a hydraulic cylinder acts at right

A mechanical advantage may be obtained in a hydraulic system by using a piston

Figure 24 Pascal’s Law

Figure 26 Astronaut on the Moon

FORCE AND WEIGHT

1 daN = 10 Figure 28 Weight

The coefficient of starting friction − µstart

Newton’s Third Law

here the force F has the same amount as the weight w.