M9 Moments — notes on one page

Every Edexcel A-level Maths 9MA0 specification point in M9, read straight through: 1 point with definitions, explanations, mark-scheme wording and worked examples. Practice questions are in the printable question pack.

Checked against Edexcel 9MA0 section M9. Review basis: the qualification registry sourced from the Pearson Edexcel Level 3 Advanced GCE in Mathematics (9MA0) specification; registry verification recorded 11 July 2026.

How this checking works

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.

Moment about a pivot is force times perpendicular distance; equilibrium requires clockwise and anticlockwise moments to balance.

Worked example

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.

1.The beam's weight acts at its midpoint, $2\,\text{m}$ from $A$ .
2.Taking moments about $A$ , $R_B(4)=120(2)$ , so $R_B=60\,\text{N}$ .
3.Vertical equilibrium gives $R_A+R_B=120$ , hence $R_A=60\,\text{N}$ .

Answer: Upward force at $A=60\,\text{N}$ ; Upward force at $B=60\,\text{N}$

Common mistakes

Don't use $Fd\cos\theta$ when the stated angle makes $Fd\sin\theta$ the perpendicular moment.
Don't take moments using the sloping distance to a force instead of its perpendicular distance from the pivot.

Exam tip. Choose a pivot that removes an unknown force, assign moment directions consistently and also check vertical equilibrium.