Moments (Turning Effect of a Force)

A moment is the turning effect of a force. Pushing a door near the handle turns it easily because the force is applied far from the hinges (the pivot).

Key ideas

• Pivot: the point an object turns about (e.g. door hinge, seesaw centre).
• Moment of a force: size of the turning effect. Formula: $\text{moment} = F \times d_\perp$, where $F$ is the force (N) and $d_\perp$ is the perpendicular distance (m) from the pivot to the line of action of the force. Unit: N m.
• Direction: moments can be clockwise (CW) or anticlockwise (ACW).

Principle of moments (equilibrium)

When an object is balanced (in equilibrium), there is no resultant force and no resultant moment. The clockwise moments equal the anticlockwise moments:

$$\sum M_{\text{clockwise}} = \sum M_{\text{anticlockwise}}$$

Everyday examples

• Door handles far from the hinge give a larger moment for the same push.
• A longer spanner makes loosening a nut easier.
• On a seesaw, a lighter person can balance a heavier person by sitting further from the pivot.

Simple experiment

Balance a metre rule on a knife edge at the 50 cm mark. Hang a 100 g mass (≈ 1.0 N) at 30 cm. Predict the balancing moment on the other side (distance from 50 cm), then add masses and adjust positions until level. You will find CW moments = ACW moments when the rule is level.