Moments is Year 13 only. It deals with rigid bodies such as rods, planks and ladders that can turn as well as slide, and questions often combine it with friction.
Start with one question on moments. Stuck? Take a hint. No sign-in needed.
Take moments (light rods and uniform planks). A light rod of length \(5\) m balances on a pivot at its centre. A \(50\) N weight hangs \(1.2\) m to the left of the pivot. How far to the right of the pivot must a \(30\) N weight hang for the rod to balance?
Take moments (light rods and uniform planks). A uniform plank of length \(6\) m and weight \(120\) N rests horizontally on supports at A and B, \(1\) m and \(5\) m from its left end. A load of \(60\) N is placed \(4\) m from the left end. Find the reaction at B.
Take moments (light rods and uniform planks). A uniform plank of length \(5\) m and weight \(80\) N rests horizontally on supports at A and B, \(0\) m and \(4\) m from its left end. A load of \(40\) N is placed \(3\) m from the left end. Find the reaction at B.
Take moments (light rods and uniform planks). A uniform plank of length \(8\) m and weight \(200\) N rests horizontally on supports at A and B, \(1\) m and \(7\) m from its left end. A load of \(100\) N is placed \(2\) m from the left end. Find the reaction at B.
Take moments (light rods and uniform planks). A light rod of length \(4\) m balances on a pivot at its centre. A \(30\) N weight hangs \(1.5\) m to the left of the pivot. How far to the right of the pivot must a \(36\) N weight hang for the rod to balance?
This topic is A Level only: it is not on the AS exam.
Year 12 (AS content)
None: moments starts in Year 13.
Year 13 (full A Level only)
The moment of a force about a point
Equilibrium of rigid bodies: resolving and taking moments
Uniform and non-uniform rods, including when a rod is about to tilt
Problems with friction, such as a ladder against a wall
Worked examplemedium3 marks
A steering wheel is acted upon by two forces: $10 \text{ N}$ applied at a perpendicular distance of $0.2 \text{ m}$ clockwise from the centre, and $15 \text{ N}$ applied at a perpendicular distance of $0.15 \text{ m}$ anticlockwise from the centre. Find the resultant moment and state its direction.
Mark scheme and worked answer
M1 for calculating the individual moments: $10 \times 0.2 = 2 \text{ N m}$ (CW) and $15 \times 0.15 = 2.25 \text{ N m}$ (ACW).
M1 for finding the net moment by subtracting the smaller from the larger: $2.25 - 2.0 = 0.25 \text{ N m}$.
A1 for stating the resultant moment is $0.25 \text{ N m}$ anticlockwise.
M1 for finding the net moment by subtracting the smaller from the larger: $2.25 - 2.0 =$ N m.
Every board examines the same A Level Maths content, set by the Department for Education. Only the paper it appears on and the section numbering differ.
Three examples from the question bank, one with its full mark scheme open. Every question comes with a step-by-step mark scheme (M, A and B marks) once you start practising.
Question 1easy2 marks
A force of $12\text{ N}$ acts perpendicular to a rod at a point $0.4\text{ m}$ from the pivot. Find the moment about the pivot.
A uniform ladder of length $5\text{ m}$ and mass $15\text{ kg}$ rests against a smooth vertical wall with its foot on rough horizontal ground. The ladder makes angle $60°$ with the ground. Find the minimum coefficient of friction $\mu$ needed to prevent the ladder from slipping. Take $g = 9.8\text{ m s}^{-2}$.
Full worked solution Free, no sign-in
Let $R$ = reaction from ground, $S$ = reaction from wall, $F$ = friction. Weight $W = 15g = 147\text{ N}$ at midpoint. Vertical: $R = W = 147\text{ N}$ M1 A1. Take moments about foot of ladder: $S \times 5\sin 60° = W \times 2.5\cos 60°$ M1. So $S = \tfrac{W \times 2.5\cos 60°}{5\sin 60°} = \tfrac{W}{2\tan 60°} = \tfrac{147}{2\sqrt{3}} = 42.4\text{ N}$ A1. Horizontal: $F = S = 42.4\text{ N}$. Min $\mu = \tfrac{F}{R} = \tfrac{42.4}{147} = 0.289$ M1 A1.
Every question here has a full worked solution.See them all →
Question 3hard6 marks
A uniform ladder $AB$ of length $6\text{ m}$ and mass $20\text{ kg}$ rests against a smooth vertical wall with its foot on rough horizontal ground. The ladder makes angle $70°$ with the ground. Find (i) the reaction at the wall, and (ii) the minimum coefficient of friction at the ground. Take $g = 9.8\text{ m s}^{-2}$.
These skills sit in the Mechanics unit of the UK A Level practice engine. Pick any mix of them, set the difficulty, and check each answer against its mark scheme.
Moments & the turning effectEquilibrium of rigid bodiesNon-uniform rods
Moments can come up on these papers (from each board's paper structure). We haven't mapped individual questions yet, so open a recent paper and look for it.
Is moments on the AQA, Edexcel and OCR A Level Maths exams?
Yes. Moments is part of the A Level Maths content that every board examines: AQA section S, Edexcel Mechanics 9, OCR 3.04. It is assessed in AQA Paper 2; Edexcel Paper 3, Section B; OCR A Paper 3, mechanics section.
Is moments Year 12 or Year 13 content?
Moments is A Level only, so it is usually taught in Year 13 and is not on the AS exam.
Where should I take moments about?
Take moments about a point where an unknown force acts, so that force has no moment. This often removes one unknown and makes the algebra much shorter.
A Level Math Revision