Moments

This lesson covers: 

  1. What a moment is and how it causes rotation
  2. How to calculate a moment
  3. The principle of moments and rotational equilibrium

Forces can cause objects to rotate

Diagram showing a pivot point and turning effect with a force acting on a seesaw.

A pivot point is the point around which an object rotates in a clockwise or anticlockwise direction, like the middle of a seesaw.

When a force acts on an object that can rotate around a pivot, it creates a turning effect.

This turning effect is called a moment and is measured in newton-metres (Nm).

Calculating moments

The size of the moment depends on two variables:

  1. Force (F) - measured in newtons (N).
  2. Perpendicular distance from the pivot (d) - measured in metres (m).


The formula to calculate moments is:

Moment (Nm) = Force (N) × Perpendicular distance from pivot (m)


The greater the force or distance from the pivot, the greater the resulting moment.

Calculating moments example

Diagram showing a seesaw with a weight of 300 N at a distance of 1.5 m from the pivot.

For example a child on a seesaw has a weight of 300 N and a distance of 1.5 m from the pivot.


Step 1: Formula

Moment (Nm) = Force (N) × Perpendicular distance from pivot (m)


Step 2: Substitution 

Moment (Nm) = 300 × 1.5


Step 3: Correct evaluation

Moment (Nm) = 300× 1.5 = 450 Nm

Moment = 450 Nm in a clockwise direction.

Balanced and unbalanced moments

For an object to be stable and remain stationary when rotated on a pivot, the sum of anticlockwise moments must equal the sum of clockwise moments.

When moments are balanced, there is no net rotational effect.

Unbalanced moments result in rotation around the pivot.

Balanced moments means no rotational movement

Diagram showing a balanced seesaw with 450 N force at 1 m and 300 N force at 1.5 m from the pivot.

Anti-clockwise moment: 

moment = 450 x 1 = 450 Nm


Clockwise moment:

moment = 300 x 1.5 = 450 Nm


The anticlockwise moment = the clockwise movement so there is no rotational movement.

Unbalanced moments means there is rotational movement

Diagram showing balanced and unbalanced moments on a seesaw with weights and distances.

Anticlockwise moment:

moment = 500 x 1 = 500 Nm


Clockwise moment:

moment = 300 x 1.5 = 450 Nm


The anticlockwise moment is greater than the clockwise moment so the seesaw moves anticlockwise around the pivot.