A moment is the turning effect of a force

Moments, Couples & Equilibrium — AQA A-Level Physics

Key Definition

Moment — The turning effect of a force about a pivot. Moment = Force times perpendicular distance from the pivot. Unit: N m.

M = F \times d

$M$: moment (N m)
$F$: force (N)
$d$: perpendicular distance from the pivot to the line of action of the force (m)

The distance must be the perpendicular distance from the pivot to the line of action of the force.
If the force is not perpendicular to the distance, use the component: $Moment = F d \cos(\theta)$, where theta is the angle between the force and the perpendicular.
A door handle is placed far from the hinge to maximise the distance and therefore the moment for a given force.

Worked Example

A uniform metre rule is pivoted at the 50 cm mark. A 0.5 kg weight is suspended at the 80 cm mark. Calculate the turning moment about the pivot.

Show Solution

Calculate the weight

$$W = mg = 0.5 \times 9.81 = 4.9 \text{ N} \approx 5 \text{ N}$$

Find the perpendicular distance

$Distance = 80 cm - 50 cm = 30 cm$

Calculate the moment

$$M = 5 \text{ N} \times 30 \text{ cm} = 150 \text{ N cm}$$

Answer

$Moment = 150 N cm (or 1.5 N\;\text{m}).$

Examiner Tips and Tricks

Draw all the forces on the diagram before calculating moments.
Not all forces provide a turning effect -- forces whose line of action passes through the pivot have zero moment.
Exam questions sometimes include extra forces to test this.