Chapter 5 - Refraction through a Lens
Moment of a Force and Equilibrium
Force causes:
• Change in state of body
• Change in shape and size of body
Types of Motion:
1. Translatory Motion
2. Rotatory Motion
1. Translatory Motion
i) If force is applied on a rigid body and the body starts moving in a straight path in the direction of motion, it is called translatory motion.
ii) In this type of motion, the entire body covers the same distance in the same time.

2. Rotatory Motion
i) If a body is pivoted at a point and a force is applied on a suitable point, it rotates the body about the axis passing through the pivoted point. This motion of the body is called rotatory motion.
ii) In rotatory motion, different parts of the body cover different distances in the same time.

Moment of Force or Torque (Also called Turning Effect)
Symbol: τ (Tau)
Factors affecting torque:
• Force
τ ∝ F
• Perpendicular distance of force applied from the pivoted point
τ ∝ S⊥
Therefore,
τ = F × S⊥
Torque is defined as the product of the force applied and the perpendicular distance of the force from the pivoted point.
Unit:
SI Unit: Newton metre (Nm)
CGS Unit: dyne centimetre (dyne cm)
Relationship:
1 N = 10^5 dyne
1 m = 100 cm
Therefore,
1 Nm = 10^5 × 100 dyne cm
1 Nm = 10^7 dyne cm
Nature:
Vector Quantity
Types of Moment:
1. Clockwise Moment
2. Anticlockwise Moment
Clockwise Moment:
When a force is applied to a body pivoted at a point and the body moves in the direction of motion of the hands of a clock, it produces clockwise moment.
• It is negative (-ve).
• It causes inward motion.
Anticlockwise Moment:
When a force is applied to a body pivoted at a point and the body moves in the anticlockwise direction, the moment produced is called anticlockwise moment.
• It is positive (+ve).
• It causes outward motion.
Changing the Direction of Torque:
i) By changing the direction of force.
Center of Gravity
Centre of Gravity
Centre of Gravity is the position where the net weight (sum of all weights) in a body acts.
$$W = W_1 + W_2 + W_3 + W_4 + \cdots$$
“The centre of gravity (CG) of a body is the point about which the algebraic sum of moments of weights of all the particles constituting the body is zero.”
The entire weight can be considered to act from this point.
FACTS REGARDING CG
1. The position of the centre of gravity depends upon the shape of the body because the concentration or distribution of masses is different.
2. The centre of gravity may or may not lie on the body.
3. The center of gravity of a body is the point from where the net weight of the body is going to act.
The position of the centre of gravity determines the stable equilibrium of the body.
Lower the position of the centre of gravity, the more stable the body will be.
Uniform Circular Motion
