Moment of force
The turning effect of force is called moment of force.

The moment of force depends on the following factors.

The size (magnitude) of the force
The perpendicular distance between the line of action of the force and the turning point which is called the pivot.
We calculate the moment of force by using the following formula

Moment of force = force * perpendicular distance from pivot to the line of action of the force
Moment=F * d

Moment is measured in newton meters(Nm).

One force on its own isn’t much use to us. We normally look at situations where turning effects are balanced (or not!).

Let’s look at the example below and find the missing force F:

If the system is balanced, the anticlockwise turning effect of force F must equal the clockwise turning effect:

clockwise moment = anticlockwise moment

Clockwise moment = 5 N × 0·50 m = 2·50 Nm.

Anticlockwise moment = F × 0·25 m = 2·50 Nm
Force F = 2·50 Nm ÷ 0·25 m = 10 N

In order to balance the 5 N force acting at 0·5 m from the pivot, we require 10 N acting in the opposite direction but at 0·25 m.

Unbalanced Forces

Sometimes moments can easily become unbalanced – even when we don’t want them to!

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Click here to read the writing!

In these unfortunate examples, it would seem that in loading the cart, some of the boxes must have slipped to the back – further away from the pivot – greatly increasing their turning effect. In the case of the lorry, its weight wasn’t enough to balance the heavy bricks.

The result was the lifting of the donkey – who must have been very surprised! For the lorry, it was lucky nobody was hurt.

Sometimes more than one force acts on the same side of the pivot. Their overall turning effect is easy to work out.

The 2 N force has a moment of 2 × 0·2 m = 0·4 Nm clockwise.
The 5 N force has a moment of 5 × 0·5 m = 2·5 Nm clockwise.

Their combined moment = 0·4 Nm + 2·5 Nm = 2·9 Nm clockwise.

Moments can just be added, but they must act in the same direction.

Moments Summary

The turning effect (or moment) of a force is given by:
moment = force × perpendicular distance from pivot

The normal units used for force and distance are newtons andmetres respectively, so the usual unit for moment is the newton-metre (Nm)

Another name for a pivot is fulcrum.

Moments can either be clockwise or anticlockwise.

When more than one force acts in the same direction, their overall turning effect is just the sum of their moments.

When forces act in a different direction, yet still balance, the total turning effect in each direction will be the same:
sum of clockwise moments = sum of anticlockwise moments

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Taking a QUIZ about this lesson

Moment Quiz

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