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How to calculate moments

Jonny Nelson introduces an animated explanation of moments, levers and gears

A force or system of forces may cause an object to turn. A is the turning effect of a force. Moments act about a point in a clockwise or anticlockwise direction. The point chosen could be any point on the object, but the , also known as the fulcrum, is usually chosen.

A plank balances on a pivot. There are identical boxes, or objects at each end of the plankm, with two arrows point downwards from the boxes. Curved arrows at the ends indicate possible rotation.
Figure caption,
The anticlockwise moment acts downward on the left, and the anticlockwise moment acts downwards on the right

The of a moment can be calculated using the equation:

moment of a force = force × distance

This is when:

  • moment is measured in newton-metres (Nm)
  • force is measured in newtons (N)
  • distance is measured in metres (m)

It is important to remember that the distance is the perpendicular distance from the pivot to the line of action of the force.

A plank balances on a central pivot, with boxes at each end. Lines cross through the middle of the boxes and pivot, with arrows showing the distance between them.

Example

A simple image of a door with handle shows a curved arrow indicating that handle is pushed down on, or turned.

A force of 15 N is applied to a door handle, 12 cm from the pivot. Calculate the moment of the force.

First convert centimetres into metres:

12 cm = 12 ÷ 100 = 0.12 m

Then calculate using the values given in the question:

moment of a force = force × distance

moment = 15 × 0.12

moment = 1.8 Nm

Question

A force of 40 N is applied to a spanner to turn a nut. The perpendicular distance is 30 cm. Calculate the moment of the force.

A spanner is turning nut. The curved arrow at bottom of spanner indicates direction of turn.