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

The anticlockwise 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)

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.

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.

Reveal answer

\[M = F~d\]

\[30~cm = 0.30~m\]

\[M = 40 \times 0.30\]

\[M = 12~Nm\]