Moments

Section M9

1 spec leaf

Notes and three levels of exam-style practice for each registered specification leaf in this section.

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M9.1

Understand and use moments in simple static contexts.

The moment of a force about a point is $F d$ , where $d$ is the perpendicular distance from the point to the force's line of action; state whether it is clockwise or anticlockwise when required.
For a rigid body in equilibrium, choose a pivot that removes unknown forces where possible, set total clockwise moments equal to total anticlockwise moments, then use force equilibrium.
A uniform rod's weight acts at its midpoint, while a non-uniform body's weight acts at its stated centre of mass; contact forces act at their contact points.
A common error is to use the distance along a rod instead of the perpendicular distance to the line of action, or to omit a force whose line of action does not pass through the pivot.

Tier 1 · Easy

2 marks

ORIGINAL

A $12\,\text{N}$ force acts perpendicular to a spanner at a distance $0.35\,\text{m}$ from a nut. Find the magnitude of its moment about the nut.

Tier 2 · Standard

4 marks

ORIGINAL

A uniform horizontal beam $AB$ has length $4\,\text{m}$ and weight $120\,\text{N}$ . It is supported vertically at $A$ and $B$ . Find the upward force at each support.

Tier 3 · Hard

7 marks

ORIGINAL

A uniform ladder of length $5\,\text{m}$ and weight $240\,\text{N}$ rests with its lower end on rough horizontal ground and its upper end against a smooth vertical wall. The ladder makes an angle of $60^\circ$ with the ground and is in limiting equilibrium. Find the force exerted by the wall and the least coefficient of friction at the ground.