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LECTURE: 02
UNIT – I Basics of mechanics and force system
Force – unit, representation as a vector and by Bow’s notation, characteristics

and effects of a force, Principle of transmissibility of force, Force system and its
classification.
.
FORCE:
 An external agent which tends to change or actually changes the state of a

body (at rest or in motion) or causes deformation in the body.
UNITS OF FORCE:
The two commonly used units of force are:
1. Absolute units
2. Gravitational units
Absolute units of Force :

 The absolute units of force are based on Newton’s 2nd law of motion.
 According to Newton’s 2nd law of motion.
Force=Mass × Acceleration
Because the mass and acceleration are measured differently in different

systems of units, so the units of force are different for different system.
 In the F.P.S. (Foot-Pound-Second) unit system, the absolute unit of force

is a poundal, which is that much force, as produces an acceleration of 1 ft
/ sec2 for a mass of one pound.
1 Poundal = 1 Pound × 1ft/sec2

= Pound ft/sec2
 In the C.G.S. (Centimetre-Gram-Second) unit system, the absolute unit of
force is Dyne , which is that much force as produces an acceleration of 1
cm/sec2 for a mass of one gram.
1 Dyne = 1 gm × 1cm/sec2
= gm cm/sec2
 In the M.K.S. (Metre-Kilogram-Second) unit system ,the absolute unit of

force is a Newton (denoted by N ), which is that much force as produces an
acceleration of 1 m/sec2 in for mass of one kilogram.
1 Newton = 1kg × 1 m/ sec2

= 1000 gm × 100 cm /sec 2
= 105 gm cm /sec2
1N = 105 Dynes
Gravitational units of Force :

 These units depend upon the weight of a body (i.e., the force with which
the body is attracted towards the centre of the earth).
 The weight of a body of mass m is mg, where g is the acceleration due to

gravity.
So the gravitational units of force in different systems of units are :
In F.P.S. Pound weight ( lbf )
C.G.S. Gram weight (gmf)
M.K.S. kilogram weight (kgf)
1 kgf = 9.81 newtons (app.)

CHARACTERISTICS OF FORCE
 The quantities by which a force is fully represented are known as the

characteristics of a force. These are also called elements of a force.
i) Magnitude: The quantity of force e.g. 10 N, 100 kN etc.
ii) Direction: It is the line along which the force acts. It is also called as
line of action of the force.
iii) Point of application: The point at which the force acts on the body.
iv) Sense or Nature:
 Pull: If the arrow head is pointed away from the point of application, the
nature of the force is pull.
 Push: If the arrow head is pointed towards the point of application, the
nature of the force is push
Consider a ball laying on a plane and a force of 10N is acting on it.

EFFECTS OF FORCE
 It may change the state of a body i.e. the state of rest or state of motion.
 It may accelerate or retard the motion of a body.
 It may turn or rotate the body on which it acts.
 It may deform the body on which it acts.
REPRESENTATION OF A FORCE
A force is a vector quantity. It has both magnitude and direction. It can be

represented in two ways:
1. Vector Representation
2. Bow’s Notation
1. Vector Representation:
Consider a force of 15N acting on a body .This can be shown in vector

representation. Here the length of the line ab shows the magnitude of the
force i.e. 15N drawn to some scale and the arrow head shows the direction
of the force.
2. Bow’s notation:
In this method of representation of force, Capital alphabets are put on either

side of the line of action of the force. The placing of letters is done
clockwise or anticlockwise.
Two forces 10N and 15 N are acting on a body .the letters a,b and c are
put on either side of the line of action of forces in anticlockwise direction.
The force 10N is then called force ab and force 15N as force bc. The vector
diagram of forces is shown.
PRINCIPLE OF TRANSMISSIBILITY OF FORCE
 It states that, “If a force acts at a point on a rigid body, it is assumed to act
at any other point on the line of action of force within the same body”.
 As per this principle force of push nature can be made pull by extending
the line of action of a force.
FORCE SYSTEM
A force system is a collection of forces acting on a body in one or more planes.
According to the relative positions of the lines of action of the forces, the forces
may be classified as follows:
1. Coplanar Collinear force system: The force system in which forces lies on
the same plane and act along the same line of action are known as Coplanar
Collinear force system.
2. Coplanar Concurrent force system: The force system in which forces lies on
the same plane and meet at a point are known as Coplanar Concurrent force
system.
3. Coplanar Non-concurrent force system: The force system in which forces

lies on the same plane but meet at different points are known as Coplanar
Concurrent force system.
3. Coplanar parallel force system:
(i) Like parallel force system: The force system in which forces lies on the same
plane and are parallel to each other acting in same direction are known as
Coplanar Like parallel force system.
(ii) Unlike parallel force system: The force system in which forces lies on the
same plane and are parallel to each other but acting in opposite direction are
known as Coplanar Unlike parallel force system.
5. Non-coplanar concurrent force system: The force system in which forces

lies in different planes but meet at a point are known as Non-coplanar Concurrent
force system.
6. Non-coplanar parallel force system: The force system in which forces lies in
different planes but are parallel to each other are known as Non-coplanar parallel
force system.
7. General force system: The force system in which forces act in different planes
and they do not possess one single point of concurrency are known as General
force system.

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LECTURE: 02

UNIT – I Basics of mechanics and force system

Force – unit, representation as a vector and by Bow’s notation, characteristics

 An external agent which tends to change or actually changes the state of a

The two commonly used units of force are:

Absolute units of Force :

Because the mass and acceleration are measured differently in different

 In the F.P.S. (Foot-Pound-Second) unit system, the absolute unit of force

1 Poundal = 1 Pound × 1ft/sec2

 In the M.K.S. (Metre-Kilogram-Second) unit system ,the absolute unit of

1 Newton = 1kg × 1 m/ sec2

Gravitational units of Force :

 The weight of a body of mass m is mg, where g is the acceleration due to

So the gravitational units of force in different systems of units are :

In F.P.S. Pound weight ( lbf )

C.G.S. Gram weight (gmf)

M.K.S. kilogram weight (kgf)

1 kgf = 9.81 newtons (app.)

 The quantities by which a force is fully represented are known as the

i) Magnitude: The quantity of force e.g. 10 N, 100 kN etc.

iv) Sense or Nature:

Consider a ball laying on a plane and a force of 10N is acting on it.

A force is a vector quantity. It has both magnitude and direction. It can be

Consider a force of 15N acting on a body .This can be shown in vector

In this method of representation of force, Capital alphabets are put on either

A force system is a collection of forces acting on a body in one or more planes.

3. Coplanar Non-concurrent force system: The force system in which forces

5. Non-coplanar concurrent force system: The force system in which forces

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