CSEC PHYSICS

Definitions, Formulae & Equations

Physical quantity Base SI unit

Mass (m) Kilogram (Kg)

Length (l) Metre (m)

Time (t) Second (s)

Current (I) Ampere (A)

Temperature (T) Kelvin (K)

Amount of sub. (n) Molar (mol)

 Luminous Intensity (L) Candela (cd)

Number Prefix Number Prefix

10 −9 nano (n) 10 3 Kilo (k)

10 −6 micro (μ) 10 6 Mega (M)

10 −3 milli (m)

Scalar Vector

Mass (m) Kilogram (Kg)

Length (l) Metre (m)

Time (t) Second (s)

Current (I) Ampere (A)

Temperature (T) Kelvin (K)

Amount of sub. (n) Molar (mol)

 Luminous Intensity (L) Candela (cd)

Kinematics
Average Speed, s=ΔdΔts=ΔdΔt, d is distance travelled
Average Velocity, v=ΔxΔtv=ΔxΔt, x is displacement
Acceleration, a=ΔvΔta=ΔvΔt
v=u+atv=u+at
x=ut+12at2x=ut+12at2
v2=u2+2axv2=u2+2ax
s=12(u+v)ts=12(u+v)t

Information that you have

Equations of motion to use
s u v a t

v=u+atv=u+at

s=ut+12at2s=ut+12at2

s=12(u+v)s=12(u+v)

v2=u2+2asv2=u2+2as

vfreefall=√2gh
If a car is driving around a circle at a constant speed, its velocity is not constant! The
car is accelerating! Why? Because velocity is a vector (has both magnitude and
direction). When the car is travelling around the circle, its direction is changing
constantly.

Forces and Turning effect of Force

Newton’s First Law: A body continues to stay in its state of rest or uniform motion in a
straight line as long as there is no net force acting on the body.
Newton’s Second Law: The acceleration of an object is directly proportional to the net
force acting on it and inversely proportional to its mass.

Newton’s Third Law: For every force object A acts on object B, object B will exert an
equal and opposite force on object A giving rise to reaction force.
M=FdM=Fd, M = moment, d = perpendicular dist. from force to pivot
Principle of moment: sum of anti-clockwise moment = sum of clockwise
moment. →→ rotational equilibrium.
Mass, Weight and Density
w=mgw=mg
ρ=mVρ=mV
Pressure 
P=FAP=FA
Pfluid=hρgPfluid=hρg
Hydraulic press: F1A1=F2A2F1A1=F2A2
Boyles’ law: P1V1=P2V2P1V1=P2V2

Work, Energy and Power

W=FdW=Fd
P=Wt=FvP=Wt=Fv
Ek=12mv2Ek=12mv2
Eg=mghEg=mgh, g = 9.81 ms−2ms−2
Conservation of energy: Initial energy = final energy

Thermal Physics
PV∝TPV∝T
P1V1=P2V2P1V1=P2V2
E=mcΔTE=mcΔT
Efusion=mLfusionEfusion=mLfusion
Evap.=mLvap.Evap.=mLvap.
Temperature can be measured using the following methods:

 Expansion of fixed mass of liquid

 Changes in resistance of a piece of metal
 Expansion of gas at constant pressure
Why is there constant temperature during melting?

 During melting, heat energy is used to weaken the attraction between the
solid particles and not used to increase the kinetic energy of the particles.
When a thermometer is placed into hot water, why does the reading drops first then
increase?

 The glass bulb expands before the mercury expands.

Good radiator of heat
  Black surface
 Rough surface

Waves, Reflection and Refraction of

light, Converging lens, Electromagnetic
Spectrum, Sound
v=fλv=fλ
f=1Tf=1T
Law of reflection: θi=θrθi=θr
Snell’s Law: n1sinθ1=n2sinθ2n1sin⁡θ1=n2sin⁡θ2
Refractive index: n=cvn=cv
Denser to less dense medium: Light ray bends away from normal

Less dense to denser medium: Bends towards normal

1<n(λred)<n(λgreen)<n(λblue)1<n(λred)<n(λgreen)<n(λblue)
Critical angle: sinθc=n2n1sin⁡θc=n2n1, n2n2 is smaller than n1

Magnification: 
M=hiho=dido
Note:
 An image that is real is always inverted!
 An image that is virtual is always upright!

When a water wave moves from deep to shallow,

 wavelength become shorter
 Frequency remains the same (Freq. of water wave only depends on
SOURCE)
 Speed becomes slower

Factors that affect speed of sound

 Temperature – Higher temperature = higher speed of sound
 Medium – The denser the medium, the higher the speed of sound
 Humidity – Sound travels faster in higher humidity conditions

Characteristics of Image formed on plane mirror

 Same size
 Laterally inverted
 Image is virtual
Electricity and D.C. Circuits
ϵ=WQϵ=WQ
V=WQV=WQ
I=QtI=Qt
R=VIR=VI (IMPT: It’s ratio, NOT gradient)
R=ρLAR=ρLA
Series: Rtotal=R1+R2+…Rtotal=R1+R2+…
Parallel: 1Rtotal=1R1+1R2+…1Rtotal=1R1+1R2+…
P=VI=I2R=V2RP=VI=I2R=V2R
E=Pt=(VI)tE=Pt=(VI)t

Electromagnetic force and Electromagnetic
Induction:
Transformer:
VpVs=NpNsVpVs=NpNs
VpIp=VsIsVpIp=VsIs

Operation of transformer:

 Alternating current supplied to primary coil

 Alternating current causes iron core to magnetise and magnetic field to
change
 Magnetic fields follow iron core and link to secondary coil
 Hence, emf is induced in the secondary coil by electromagnetic induction
due to the changing magnetic fields

Left hand rule for motor:

Right hand rule for generator/dynamo:

Right hand grip rule: (To determine direction of magnetic field/current)

Ways to increase emf in solenoid:

1. Use a stronger magnet
2. Increase the speed of moving the magnet
3. Increase the number of turns in the coil

Ways to increase emf in a.c. generator:

1. Decrease distance between magnet and coil
2. Use a stronger magnet
 3. Increase frequency of rotation of the coil (Double freq. = double max.
e.m.f. and halving T)
4. Increase number of turns in the coil (Double no. of turns = double max
e.m.f.)

Radioactivity & The Nuclear Atom

Half life:  (n is number of half-life)

Nfinal /Ninitial=(1/2)n

SECTION A: MECHANICS

Measurements
Quantity and symbol SI unit
mass m kilogram [ kg ]
length l metre [ m ]
time t second [ s ]
current I Ampere [ A ]
temperature T Kelvin [ K ]

Number Prefix
Prefix and symbol Number
nano n 10 9 [ divide by 1 000 000 000 ]
micro µ 10 6 [ divide by 1 000 000 ]
milli m 10 3 [ divide by 1 000 ]
kilo k 10 3 [ times by 1 000 ]
mega M 10 6 [ times by 1 000 000 ]

Scalars and Vectors

A scalar is a quantity that has only magnitude.

A vector is a quantity that has both magnitude and direction.

Examples of scalars Examples of vectors
mass, length, time, temperature, area, volume, speed, force, momentum, displacement, velocity,
pressure, distance work, energy, power, resistance, acceleration, weight

current

Density and relative density

Density is the mass per unit volume; meaning how much matter or particles are in a given volume of
space. Density is a scalar.

Relative density is a ratio of the density of a substance to the density of a base substance such as
water.

mass
density =
volume
m density  [ kg m 3 ]
 =
V mass m [ kg ]
density of substance volume V [ m3 ]
relative density =
ensity of base substance relative density ρR [ ]
ρ
ρ R = substance
ρbase
 Statics

The moment of a force about a point is the product of the force and the perpendicular distance of line
of action from the point. Moment is a vector.

Common devices that use the principle of moments are spanner, wheelbarrow, crowbar, bottle
opener, claw hammer

Equilibrium is the state of a body at rest or in uniform motion, the resultant of all forces on which is
zero. In equilibrium, the net force in all directions is zero.

Condition of equilibrium
1. The sum of the forces in any direction is equal to the sum of the forces in the opposite direction
(translational equilibrium).

2. The sum of the clockwise moments about any point is equal to the sum of the anticlockwise
moments about that same point (rotational equilibrium).

The centre of gravity is the point associated with an object where all the weight seems to act for all
orientations.

The position of the center of gravity determines the stability of an object: when the center of gravity is
high the object will be more unstable and if it is low it will be more stable.

The extension of an elastic body, such as a spring or wire, is directly proportional to the stretching
force, if the elastic limit is not exceeded’. Hooke’s law: means, as load increases then extension will
also increase. Extension is a scalar.

moment T [Nm]
moment = force × perpendicular distance from pivot
distance d [m]
T = F×d
force F [N]
force = elastic constant × extension elastic constant k [ N m 1 ]
F = k×x extension e or x [ m ]
 Dynamic: motions in a straight (Distance, displacement, speed, velocity and acceleration)

Distance is the length between two points. Distance is a scalar.

Displacement is the distance in a specific direction. Displacement is a vector.

Speed is the rate of change of distance. Speed is a scalar.

Velocity is the rate of change of displacement. Velocity is a vector.

Acceleration is the rate of change of velocity. Acceleration is a vector.

distance covered
speed =
timetaken
∆d
v =
∆t

total distace
average speed =
total time
distance d[m]
change of displacement
velocity =
time
∆s displacement s or x [ m ]
v =
∆t

total displacement speed or velocity v [ m s 1 ]

average velocity =
total time

distance travelled = area under the graph acceleration a [ m s 2 ]

1 2 v 2−u 2
s = ut + at =
2 2a

change of velocity
acceleration =
time
∆v v−u
a = =
∆t t
 Linear momentum. Conservation
The linear momentum of a body is the product of its mass and its velocity. Momentum is a vector.

The law of conservation of linear momentum states that, in the absence of external forces, the total
momentum of a system of bodies is constant; the total momentum before is equal to the total
momentum after.

momentum = mass × velocity

p = m×v
momentum p [ kg m s 1 ]
Δp = m v  m u

conservation of momentum
m A u A + mB u B = ( m A + mB ) v

Newton’s laws of motion. Impulse

A body continues in its slate of rest or uniform motion in a straight line unless acted on by a resultant
force. This is Newton’s first law.

The rate of change of momentum of a body is proportional to the applied force and takes place in the
direction of the force. This is Newton’s second law.

If body A exerts a force on body B, then body B exerts an equal but oppositely directed force on body
A. In other words, 'every action has an equal, but Oppositely directed reaction'. This is Newton’s
third law.

change of momentum force F[N]

Resultant force =
time
momentum p [ kg m s 1 ]
∆p mv−mu
F = = = ma
∆t t
impulse Ft [ N s]
impulse = change of momentum
NOTE: kg m s 1  N s
Ft = mv  mu
 Work, energy, power and efficiency
Work is the product of a force and the distance moved by Its point of application in the direction of
the force. Work is a scalar.

Energy is the ability to do work. Energy is a scalar.

Power is the rate of doing work or the rate of using energy. Power is a scalar.

work = force × displacement

W = Fs

Energy = force × displacement

E = Fs
work W [ J = kg m 2 s 2 ]
Ep = m g h
Energy E [ J = kg m 2 s 2 ]
1
Ek = mv2
2 1 joule (1 J) of work is done when the point of
application of a force of 1 N moves through a
Conservation of energy distance of 1 m in the direction of the force.
1 2
gh = v
2 power P [ W = kg m 2 s 3 ]

work 1 walt (1 W) is the power used in doing 1 J of

power =
time work per 1 s.

W E
P = = = Fv
t t

energy output
efficiency = =
energy input
 Weight, pressure and buoyancy
Weight is the product of mass by gravitational field strength. Weight is a vector.

Pressure is the force acting normally per unit area. Pressure is a scalar.

Archimedes' principle states that when a body is completely' or partially immersed in a fluid, it
experiences an upthrust equal to the weight of the fluid displaced.

Weight = mass × gravitational field strength

W = m×g

Force
Pressure =
Area
F
P = weight w[N]
A

Pressure in fluids = density of fluid × gravitational pressure P [ Pa = kg m  1 s 2 ]

field strength × depth in fluid
P =  g h

Archimedes’ principle
F = weight of the fluid displaced
=  g V
SECTION B: THERMAL PHYSICS AND KINETIC THEORY

Gas laws
For a fixed mass of gas at constant temperature, the pressure is inversely proportional to its volume.
This is Boyle's law.

For a fixed mass of gas at constant pressure, the volume is directly proportional to its absolute
temperature. This is Charles' law.

For a fixed mass of gas at constant volume, the pressure is directly proportional to its absolute
temperature. This is Pressure law.

1
P  or P V = constant (when T constant)
V
P1 V1 = P2 V2

V
V  T or = constant (when P constant)
T
V1 V2 temperature T [K]
=
T1 T2
pressure P [ Pa ]
P
P  T or = constant (when V constant)
T
volume V [ cm 3 ]
P1 P2
=
T1 T2

No constant (general gas law)

P1V 1 P2V 2
=
T1 T2
 Temperature and heat
Temperature is the degree of hotness or coldness. Temperature is a scalar.

The upper fixed point (100 °C) is the temperature of steam from pure boiling water at standard
atmospheric pressure.

The lower fixed point (0 °C) is the temperature of pure melting ice at standard atmospheric pressure.

Heat is thermal energy in the process of transfer from a point of higher temperature to one of lower
temperature, due to the temperature difference between them.

A body possesses thermal energy, but not heat energy. The thermal energy of a body can rise or
fall, for example by the absorption or emission of heat.

Kelvin = Celsius + 273

temperature T [ K ] or  [ °C ]
T =  + 273

Heat energy due to change of temperature

The specific heat capacity of a substance is the heat needed to change unit mass of the substance by
unit temperature. It is the property of a SUBSTANCE.

The heat capacity of a body is the heat needed to change the body by unit temperature. It is the
property of a BODY.

temperature T [ K ] or  [ °C ]
EH = m c ΔT
J
specific heat capacity c[ ] or [
kg K
ΔT = ΔѲ J
]
kg °C
EH
C = mc =
∆T J J
heat capacity C[ ] or [ ]
K °C
 Investigating specific heat capacity

mass of water mw [ g ]

mass of metal mm [ g ]

J
The specific heat capacity of a metal by the specific heat capacity of water cw [ ]
g° C
method of mixtures
J
specific heat capacity of metal cm [ ]
mw c w (❑3−❑2 ) g° C
cm =
mm (❑1−❑3 )
Temperature of hot metal  1 [ °C ]

Temperature of cold water  2 [ °C ]

Temperature of hot mixture  3 [ °C ]

voltage V [V]

current I [A]
The specific heat capacity of a metal by an
electrical method Time t [s]

J
VIt specific heat capacity of metal cm [ ]
cm = g° C
mm ( θ 2−θ1 )
Temperature of cold water  1 [ °C ]
Ee = V I t
Temperature of hot water  2 [ °C ]

Electrical energy Ee [ J ]
 mass of water mw [ g ]

mass of liquid mL [ g ]

J
The specific heat capacity of a liquid by the specific heat capacity of water cw [ ]
g° C
method of mixtures
J
specific heat capacity of metal cm [ ]
m w c w (❑3−❑2 ) g° C
cL = =
m L (❑1−❑3 )
Temperature of hot liquid  1 [ °C ]

Temperature of cold water  2 [ °C ]

Temperature of hot mixture  3 [ °C ]

Heat energy due to change of state

Latent heat is the heat energy necessary to change the state of a body without a change
of temperature.

The specific latent heat of fusion of a SUBSTANCE is the heat energy needed to change unit mass of
the substance from solid to liquid without a change of temperature.

The specific latent heat of vaporisation of a SUBSTANCE is the heat energy needed to change unit
mass of the substance from liquid to gas without a change of temperature.

mass m [ kg ]
E H = m lF or
J J
E H = m lv specific latent heat lF [ ] or l v [ ]
kg kg

Investigating specific latent heat

voltage V [V]
The specific latent heat of fusion of ice by an
electrical method current I [A]

VIt Time t [s]

lF =
mw
mass of water mw [ g ]
 The specific latent heat of vaporisation of water
by an electrical method mass of hot water m1 [ g ]

VIt new mass of hot water m2 [ g ]

lV =
m1 −m2

Evaporation and boiling

Evaporation is the escape of molecules from the surface of a liquid.

Boiling is the escape of molecules from the body of a liquid and occurs only at a particular
temperature for a given pressure

Differences between boiling and evaporation

Parameter of
Boiling Evaporation
Comparison
Boiling creates an extremely rapid movement of
Movement of water particles as this is an endothermic process Molecules are always moving, but at
Particles which signifies the addition of heat to a a much slower rate than boiling.
substance.
is a natural process; it is typically
Natural or
is an unnatural process. known as the first step in the Water
Unnatural
Cycle.
occurs all throughout the liquid due to the
Where it Occurs occurs at the surface of the liquid
addition of so much heat.
Time takes shorter period of time takes longer to complete.
requires a temperature that is greater than the
Temperature requires little change in temperature.
boiling point.
requires little to no energy being
Energy requires lots of energy being added.
added.

Factors affecting the rate of evaporation

1. Temperature. Temperature change is proportional to the rate of evaporation.

2. Humidity. Humidity is inversely proportional to the rate of evaporation.

3. Wind. Wind is proportional to the rate of evaporation.

4. Surface area. Surface is proportional to the rate of evaporation.

Thermal energy transfer

Conduction is the transfer of thermal energy between two points in a medium by the relaying of
energy between adjacent particles of the medium, with no net displacement of the particles.
Conduction occurs significantly in solids (to a greater extent in metals than in non-metals), less
in liquids, and very little in gases. Cannot occur through a vacuum.

Convection is the transfer of thermal energy between two points in a medium by the movement of the
particles of the medium due to existing regions of different density. Convection occurs in liquids and
gases. Cannot occur through a vacuum.

Radiation is the transfer of thermal energy by means of electromagnetic waves. Radiation occurs
readily through gases and through a vacuum.

Factors affecting the absorption or emission of radiation

Factors Good absorbers / emitters Good reflectors
Texture (rough or smooth) rough smooth
Colour (black or white/silver) black white/silver
Nature (dull or shiny) good emitters shiny
Area (large or small) large small
SECTION C: WAVES AND OPTICS

Wave motion
A wave is a continuous stream or regular disturbances.

A pulse is a single disturbance that propagates from point to another.

Progressive waves are those that transfer energy from one point to the next.

Latent heat is the heat energy necessary to change the state of a body without a change
of temperature.

The specific latent heat of fusion of a SUBSTANCE is the heat energy needed to change unit mass of
the substance from solid to liquid without a change of temperature.

The specific latent heat of vaporisation of a SUBSTANCE is the heat energy needed to change unit
mass of the substance from liquid to gas without a change of temperature.

mass m [ kg ]
E H = m lF or
J J
E H = m lv specific latent heat lF [ ] or l v [ ]
kg kg

Pulses, progressive waves, transverse and longitudinal waves.

The alnplituc/t of a wa\'( is the maximum displacement of the \.'ibr,llIon or ()~uJlalJon

'-,om Its mean posItion.
'OIfHS pronre..,. \.1\ eo arC' in phase 'f thf' d/~t.1n( (' b( In ('en them along the dllPctlOn of
propagation is equal to a whole number of wa l'elengths, A: IJA, 1 A, 2,1, and so on.
r ,. \ I\,.{( I1gll du'("",( llthet ~L'fl J({e' ~('fl'lrt n' L(I'nc1\\'IV

'\ lransrer-se wave is one that has vibrations perpendicular to its direction of propagation.
" longitudinal wa"e is olle th,ll has vibratIOns parallcl to its direction ofpropagaUon.
SECTION D ELECTRICITY AND MAGNETISM

Item 41 refers to the following diagram which represents a straight wire carrying a current, into the
plane of a piece of paper.

Which of the following diagrams BEST represents the magnetic field around the wire?

The unit of electrical resistance may be expressed as

(A) l o - 1 v A '
(B) I Q= 1AV
(C) l Q = 1 A V - r
(D) 1 C l = 1 W A '

Rectification can BEST be done by using a

(A) transformer
(B) capacitor
(C) transistor
(D) diode

Which of the following circuit symbols represents a fuse?

Which of the following circuit diagrams BEST represents a series arrangement?

In the circuit above, A 1, A 2, A 3, A 4 and A 5 are identical ammeters, and three equal resistors are
denoted by R. Which of the following statements would be correct?
I. The readings of A 1 and A 5, will be the same.
II. The readings of A 1, and A 2 will be the same.
III. The readings of A 3 and A 4 will be the same.
(A) III only
(B) I and II only
(C) II and III only
(D) I, II and III

Which of the following equations CANNOT be used to determine the power dissipated in a resistor?

Which of the following diagrams is a representation of the current/p.d. relationship for a metallic
conductor at a constant temperature?
In which of the following circuits will the lamp light up?
Item 52 refers to the following truth table with inputs A and It and output C.

(A) NAND
(B) NOR
(C) AND
(D) OR

Magnetic induction occurs when

(A) a magnet is suspended and points in the NS direction

(B) iron nails near a magnet become magnetized
(C) an N pole attracts an S pole
(D) an electroscope is charged

Which of the following shows the magnetic field between a bar magnet and a piece of iron?
Which of the following materials is MOST suitable for the core of an electromagnet?
(A) Steel
(B) Carbon
(C) Copper
(D) Soft iron

Which device allows one circuit to switch another circuit on or off without any direct contact between
them?
(A) Magnetic relay
(B) Electromagnet
(C) Generator
(D) Motor

Which of the following pairs of statements is true for BOTH iron and steel?

Item 53 refers to the following diagram of a simple a.c. generator.

The parts labelled X in the diagram are known as the
(A) coils
(B) slip rings
(C) armatures
(D) commutators

Item 46 refers to the following diagram.

46. Appropriate labels for W and X are

SECTION E THE PHYSICS OF THE ATOM

1. Radioactivity takes place in an atom as a result of

(A) nuclei instability
(B) a chemical reaction
(C) exposure to excess heat
(D) excess stress on the atom

2. Which of the following is true of gamma radiation?

(A) It is high energy radiation.
(B) It is not very penetrating.
(C) It has negative charge.
(D) It is a long wavelength e.m. wave

Which of the following are two properties of an a-particle?

(A) No charge, very penetrating
(B) Positive charge, very penetrating
(C) Negative charge, not very
(D) Positive charge, not very penetrating

Which of the following graphs shows how the activity of a radioactive source varies with time?
 14
3. Which of the following types of radiation is responsible for an atom of 6C changing
into an atom of 147C ?
(A) 
(B) 
(C) 
(D) Infra-red

4. In the equation E = m c2
(A) c = speed of light, m = mass of atom
(B) c = specific heat capacity of substance, m = mass of substance
(C) c = specific heat capacity of substance, m = mass lost
(D) c = speed of light, m = mass lost

5. A nuclide of zinc can be represented as 64

30 Zn. The number of electrons in a neutral atom is
(A) 30
(B) 34
(C) 64
(D) 94

6. What is the mass number, A, and atomic number, Z, of the new element formed when an alpha
particle is emitted from radium 224
88 Ra ?
AZ
(A) 222 86
(B) 224 84
(c) 226 89
(D) 230 90

7. The isotope 224

88 Ra contains
(A) 88 neutrons
(B) 140 neutrons
(C) l40protons
(D) 228 protons

Item 60 refers to information in the table below.

Nucleus Neutron number Proton number

P 126 82
Q 126 83
R 125 82
S 146 92

8. Which pair of atomic nuclei arc isotopes?

(A) P and Q
(B) Q and R
(C) P and R
(D) Q and S

9. Which of the following equations is correct?

(A) 226
88 Ra  222
88 Rn +  particle
14 13
(B) 6C  7 N +  particle
226 222
(C) 88Ra  88 Rn +  particle
14 13
(D) 6C  7 N +  particle