Moments

Section M9

Year 2

1 specification point

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

Checked against Edexcel 9MA0 section M9

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.

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M9.1

Understand and use moments in simple static contexts.

Notes

Worked answers & exam appearances →

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Explanation

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.

Tier 1 · Easy

ORIGINAL

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.

(2)

(Total for Question 1 is 2 marks)

Tier 2 · Standard

ORIGINAL

A uniform horizontal beam

AB

6\,\text{m}

long and weighs

90\,\text{N}

. It is supported vertically at

A

and

B

, and a

150\,\text{N}

load is placed

4\,\text{m}

from

A

. Find the upward force at each support.

(5)

(Total for Question 1 is 5 marks)

Tier 3 · Hard

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.

(7)

(Total for Question 1 is 7 marks)

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Answer conventions

Follow the wording on the question and its mark scheme. awrt means an appropriately rounded value is accepted; an exact answer must stay as a fraction, surd, logarithm or multiple of π when required, and a rounded decimal may be disallowed. Include requested units and forms. A cso tag protects that accuracy mark, while earlier method marks follow the question-specific dependencies.

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