Moments

A moment is a turning effect of a force. Forces can make objects turn if there is a pivot.

Think of a playground see-saw. The pivot is the part in the middle. The see-saw is level when no-one is on it, but the see-saw tips up if someone gets onto one end. It is possible to balance the see-saw again if someone else gets onto the other end and sits in the correct place. This is because the turning forces are balanced - we say the moments are equal and opposite.

Calculating moments

To calculate a moment, you need to know two things:

  • the distance from the pivot that the force is applied
  • the size of the force applied
curriculum-key-fact
moment = force × distance

Example

The diagram shows two masses balanced on a level beam. Calculate the moment on each side of the pivot.

A weight of 10N is 2m from the pivot. It has a moment of 10 x 2 = 20Nm. Another weight weighs 20N and is 1m from the pivot. The moment is 20 x 1 = 20Nm, so the two weights are balanced

On the left:

moment = force × distance

= 10 N × 2 m = 20 Nm

On the right:

moment = force × distance

= 20 N × 1 m = 20 Nm

Notice that the unit of moment is the newton metre, Nm. Do not get confused with a 'newton meter', which is another name for a force meter.

You should also notice that the two moments in the example are equal and opposite. They are both 20 Nm but the left-hand one acts in an anticlockwise direction, and the right-hand one acts in a clockwise direction. This is why the beam is balanced.

Using moments

  • A see-saw will balance if the moments on each side of the pivot are equal. This is why you might have to adjust your position on a see-saw if you are a different weight from the person on the other end.
  • If a nut is difficult to undo with a short spanner, a longer spanner will help. This is because there will be a bigger moment on the nut, when the same force is applied further from the pivot.
  • Using the same principle you can increase the moment applied by a lever or a crowbar, and this can help you move heavy objects more easily.