This mini-lesson covers AQA section S — Moments: the moment of a force (force × perpendicular distance), clockwise and anticlockwise moments, the two conditions for equilibrium of a rigid body, uniform and non-uniform rods, reactions at supports, and tilting.
A uniform rod: its weight acts at the centre. Take moments about a support to eliminate that unknown reaction.
Work through each screen, answer the questions as you go (some are wordy, some are calculations) and collect ⭐ stars. We use g = 9.8 m s⁻², and rods are rigid, with uniform rods having their weight at the centre. Press Start when you're ready.
Section S1 · moments
The moment of a force
A moment measures the turning effect of a force about a point.
moment = force × perpendicular distanceunits: newton metres (N m) · state the sense: clockwise or anticlockwise
The distance must be measured perpendicular to the line of action of the force.
If a force of F acts at an angle θ to the rod, at a distance d from the pivot, the moment is F d sin θ (only the component perpendicular to the rod turns it).
A force whose line of action passes through the pivot has zero moment — the perpendicular distance is 0.
Worked example
A force of 20 N acts perpendicular to a spanner, 0.75 m from the bolt.
Moment = 20 × 0.75 = 15 N m (clockwise, say)
Calculate
Moment of a force
1A force of 20 N acts perpendicular to a spanner at a distance of 0.75 m from the bolt. Calculate the moment about the bolt.
N m
Hint: Moment = force × perpendicular distance = 20 × 0.75.
Quick check
Perpendicular distance
?A force of 10 N acts at 30° to a rod, at a distance of 2 m from the pivot. What is the moment about the pivot?
Section S1 · equilibrium
Equilibrium of a rigid body
For a rigid body (a rod, a plank, a beam) to be in equilibrium, two conditions must hold:
1. Resolve: the resultant force is zero (so total up = total down).
2. Take moments: the total moment about any point is zero — so total clockwise = total anticlockwise.
Strategy that saves marks: take moments about a point where an unknown force acts. That force then has zero moment and vanishes from the equation, leaving one unknown.
Worked example — the seesaw
A child of mass 30 kg sits 2 m from the pivot. Where must a 40 kg child sit to balance?
Moments about the pivot: 30g × 2 = 40g × d
g cancels: 60 = 40d → d = 1.5 m on the other side.
Calculate
Balancing a seesaw
2A child of mass 30 kg sits 2 m from the pivot of a light seesaw. How far from the pivot, on the other side, must a 40 kg child sit to balance it?
m
Hint: Moments about the pivot: 30g × 2 = 40g × d. The g cancels: 60 = 40d.
Sort it
Clockwise, anticlockwise, or zero?
Tap a force description, then tap the moment it produces about the pivot.
🕐 Clockwise
🕘 Anticlockwise
0️⃣ Zero moment
Section S1 · rods
Rods, supports and reactions
A uniform rod has its weight at the centre. A non-uniform rod does not — finding where its weight acts is a standard exam question.
Worked example — a uniform rod on two supports (g = 9.8)
A uniform rod AB of length 4 m and mass 10 kg rests horizontally on supports at A and B. A particle of mass 6 kg is attached 1 m from A. Find the reactions.
Moments about A (this kills R(A) — its distance is zero):
Tilting: when a rod is on the point of tilting about one support, the reaction at the other support is zero. Set that reaction to 0 and take moments — that is the whole trick.
Calculate
Reaction at B
3A uniform rod AB of length 4 m and mass 10 kg rests on supports at A and B. A 6 kg particle is attached 1 m from A. (g = 9.8) Find the reaction at B, to 1 d.p.
4For the same rod, calculate the reaction at A, to 1 d.p.
N
Hint: Resolve vertically: R(A) + R(B) = (10 + 6)g = 156.8 N. So R(A) = 156.8 − 63.7.
Calculate
Non-uniform rod
5A non-uniform rod AB of length 3 m and weight 60 N rests on supports at A and B. The reactions are R(A) = 40 N and R(B) = 20 N. Find the distance d of the centre of mass from A.
m
Hint: Moments about A: R(B) × 3 = 60 × d, so 20 × 3 = 60d.
Quick check
Two conditions
?What are the conditions for a rigid body to be in equilibrium?
Match it
Moments in words
Tap a phrase on the left, then how it finishes on the right.
Statement
Completion
Quick check
On the point of tilting
?A plank rests on two supports and a person walks towards one end. The plank is on the point of tilting. What do you know?
Quick check
Units check
?What is the unit of a moment?
Section S1 · tilting
On the point of tilting
When a plank rests on two supports and a load moves outwards, the reaction at the far support shrinks. At the moment of tilting, that reaction is exactly zero.
Worked example
A uniform plank AB of length 8 m and mass 30 kg rests on supports at A and at C, where AC = 6 m. A man of mass 40 kg walks from A past C. How far beyond C can he go before the plank tilts?
At the point of tilting about C, the reaction at A is zero. Take moments about C:
The plank's weight acts at its centre, 4 m from A — that is 2 m on the A-side of C: anticlockwise moment = 30g × 2 = 60g
The man is x m beyond C: clockwise moment = 40g × x
Balance: 40g x = 60g → x = 60 ÷ 40 = 1.5 m beyond C (i.e. 7.5 m from A).
Why it works: setting the far reaction to zero removes one unknown, and taking moments about the support it tilts around removes the other. One equation, one unknown.
Calculate
Tilting point
6A uniform plank AB of length 8 m and mass 30 kg rests on supports at A and C, with AC = 6 m. A man of mass 40 kg walks beyond C. How far beyond C can he walk before the plank tilts?
m
Hint: At tilting, R(A) = 0. Moments about C: 40g × x = 30g × 2 (the plank's centre is 2 m on the other side of C).
Quick check
A couple
?Two equal and opposite forces act on a rod, but along different lines of action (a couple). What happens?
Recap
The big ideas to know
Moment = force × perpendicular distance (N m); a force at angle θ to the rod gives Fd sin θ
Zero moment: any force whose line of action passes through the pivot
Equilibrium of a rigid body: resultant force = 0 and total moment about any point = 0
Uniform rod: weight acts at the midpoint · Non-uniform: find where it acts by taking moments
Take moments about an unknown force to make it disappear from the equation
On the point of tilting: the reaction at the other support is zero
That is the whole of section S — Moments for AQA A-level Mathematics (7357). Press Finish to see your score.
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