What is a moment
We define the turning effect with the equation:
Moment = Force × Perpendicular distance from the pivot
Since force is measured in newtons (N) and distances in metres (m) the unit for a moment is the newton-metre (Nm).
Moments can act in two ways: clockwise or anticlockwise.
Moment = 4 N × 0·4 m
Moment = 1·6 Nm anticlockwise Moment = 4 N × 0·25 m
Moment = 1·0 Nm anticlockwise Moment = 5 N × 0·50 m
Moment = 2·5 Nm clockwise
Balancing Moments I
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
Balancing moments II
We have seen that more than one moment can act in one direction. We may sometimes wish to work out how these could be balanced.
At what distance must the 6 N force act to balance the other forces?
When balanced: sum of clockwise moments = sum of anticlockwise moments
It is easily shown that the clockwise moment = 3.0 Nm. To balance this, the anticlockwise moment must also be 3·0 Nm. So:
6 × d = 3·0
d = 3·0 ÷ 6 = 0·5 m