Forces, moments and rotation

Moments

A force or system of forces may cause an object to turn. A moment is the turning effect of a force. Moments act about a point in a clockwise or anti-clockwise direction. The point chosen could be any point on the object, but the pivot – 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.The anti-clockwise moment acts downward on the left, and the clockwise moment acts downwards on the right

The magnitude of a moment can be calculated using the equation:

moment of a force = force × distance

M = F~d

This is when:

  • moment (M) is measured in newton-metres (Nm)
  • force (F) is measured in newtons (N)
  • distance (d) is measured in metres (m)
curriculum-key-fact
It is important to remember that the distance (d) is the perpendicular distance from the pivot to the line of action of the force (see diagram).
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.The perpendicular distance is the shortest distance between the pivot and the line of action of the force

Example

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

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

First convert centimetres into metres:

12~cm = \frac{12}{100} = 0.12~m

Then calculate using the values given in the question:

M = F~d

M = 15 \times 0.12

M = 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.

M = F~d

30~cm = 0.30~m

M = 40 \times 0.30

M = 12~Nm