Turning forces are found in many everyday situations and are essential for machines to function. Levers and gears make use of these turning forces to provide an advantage.

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

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 anticlockwise direction. The point chosen could be any point on the object, but the pivot - also known as the fulcrum - is usually chosen.

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)

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).

Example

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:

\[M = F~d\]

\[M = 15 \times 0.12\]

\[M = 1.8~Nm\]

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.