Theory

Linear vs Rotational Motion

In linear motion a body moves along a straight line — its position changes. In rotational motion a body turns about a fixed axis (the pivot) — its orientation changes. A pivoted body cannot translate, only rotate.

Moment of a Force (Torque)

The turning effect of a force about a pivot is called the moment of the force or torque (τ). It depends on:

The magnitude of the applied force F.
The perpendicular distance d from the pivot to the line of action of the force.

τ = F \times d

SI unit: newton-metre (N·m). Conventionally, anticlockwise rotation is taken as positive and clockwise as negative.

Factors Affecting Torque

Larger force → larger torque (linear relation).
Larger perpendicular distance → larger torque (linear relation).
If the line of action passes through the pivot, the torque is zero.
Reversing the force direction reverses the rotation.

Worked Example

A force of 25 N is applied perpendicular to a spanner of length 20 cm.

τ = F \times d = 25 N \times 0.20 m = 5 N \cdot m

If the spanner length is doubled to 40 cm, only 12.5 N is needed for the same 5 N·m torque.

Clockwise and Anticlockwise Moments

When several forces act on the same body, the body is in rotational equilibrium when the sum of anticlockwise moments equals the sum of clockwise moments about the pivot.

\sum τ_{acw} = \sum τ_{cw}