Overview
What you’ll learn
- Calculate a moment with M = F d, using the perpendicular distance to the pivot.
- State the principle of moments and use it to balance systems.
- Explain how levers let a small effort balance or move a large load.
- Calculate gear speeds and turning moments from the ratio of teeth.
- Describe the distance-for-force trade-off in levers and gears.
Specification checklist (AQA 8463 · Edexcel 1PH0 · OCR Gateway J249)
Statements are paraphrased from the shared DfE subject content and grouped by tier. Foundation content is studied by every student; Higher statements are examined on Higher-tier papers only, and statements badged Physics only are examined in separate (triple) Physics, not Combined Science. QuizQuip is not affiliated with AQA, Pearson Edexcel or OCR.
Foundation — every student
- 12.1Describe the turning effect of a force (its moment) as force × perpendicular distance from the line of action of the force to the pivot, M = F d, in newton-metres. (Physics only)Physics only
- 12.2State and apply the principle of moments: when an object is balanced, the sum of the clockwise moments about the pivot equals the sum of the anticlockwise moments. (Physics only)Physics only
- 12.3Describe how levers transmit the turning effect of a force, and explain the trade-off: a smaller force is needed further from the pivot, but it moves through a larger distance. (Physics only)Physics only
- 12.4Explain how gears transmit rotational effects: the ratio of teeth sets the ratio of rotational speeds, and a slower-turning larger gear delivers a larger turning moment. (Physics only)Physics only
- 12.5Calculate moments, balancing distances and unknown forces using the principle of moments, and calculate gear speeds and moments from tooth numbers. (Physics only)Physics only
Key points
- 1Moment = force × perpendicular distance from the pivot: M = F d, in newton-metres (N m) — the turning effect of a force. (Physics only)
- 2Principle of moments: balanced means total clockwise moment = total anticlockwise moment about the same pivot. (Physics only)
- 3A lever is a force multiplier: effort far from the pivot balances a load close to it — but the effort moves further. (Physics only)
- 4Gears: teeth ratio sets speed ratio; the larger gear turns slower but with a larger moment, so moments multiply where speeds divide. (Physics only)
- 5Meshed gears turn in opposite directions; a chain-linked pair (bicycle) turn the same way.
- 6The distance must be perpendicular to the line of action of the force — pushing at a slant wastes turning effect.
Notes · 1 of 4
What a moment is (Physics only)
Force times perpendicular distance — the measure of turning effect.
A moment is the turning effect of a force about a pivot: M = F d, where d is the perpendicular distance from the pivot to the line of action of the force, in newton-metres (N m). Physics-only territory at GCSE — Combined Science leaves it out. The perpendicular bit matters: pushing a gate squarely across its width turns it best; pushing almost along the line of the gate barely turns it at all, because the perpendicular distance from the hinge is tiny. Doors open most easily with the handle far from the hinge — a long lever arm turns a modest push into a large moment. Similarly, a spanner with a long handle loosens a stiff nut that a short one cannot.
Notes · 2 of 4
The principle of moments
Balanced means clockwise moments equal anticlockwise moments.
When a body is balanced (not rotating), the moments on each side cancel: total clockwise moment about the pivot = total anticlockwise moment about the pivot. This is the principle of moments, and it is how you find unknown forces or distances in balanced systems. A see-saw shows it: a light child far from the pivot can balance a heavy child near it. The same law sets up the classic metre-rule practical: balance a rule on a pivot, hang known weights at measured distances, and check that force × distance adds up on both sides.
Notes · 3 of 4
Levers as force multipliers
Distance traded for force — crowbars, wheelbarrows and bottle openers.
A lever is a rigid bar pivoting about a fulcrum. Put the load close to the pivot and apply the effort far from it, and a small effort can balance a large load, because moment is force × distance. A crowbar with the load 0.10 m from the pivot and your hands 1.5 m away multiplies your push fifteen-fold. The universe keeps the books: your effort moves through fifteen times the distance the load moves, so no energy is gained — levers trade distance for force, which is why long handles make hard jobs feel easy.
Notes · 4 of 4
Gears: trading speed for moment
Teeth ratios decide who spins fast and who turns hard.
Meshed gears rotate in opposite directions, and the numbers of teeth set the speed ratio: a 20-tooth gear driving a 40-tooth gear makes the driven gear turn at half the speed. The same ratio multiplies the turning moment the other way — the slower, larger gear delivers twice the moment. This is a lever system in rotary form: speed divided is moment multiplied (an ideal, frictionless transfer keeps the product of speed and moment the same). Bicycle gears work through a chain, which keeps the two sprockets turning the same way; low gears (small front, large rear) make climbing hills easier with more pedalling, high gears the reverse.
Revise
Key terms
The words examiners expect you to use precisely.
- Moment
- The turning effect of a force: M = F d, in newton-metres (Physics only).
- Pivot (fulcrum)
- The fixed point about which an object turns.
- Perpendicular distance
- The shortest distance from the pivot to the line of action of the force.
- Principle of moments
- For a balanced body, total clockwise moment = total anticlockwise moment about the pivot (Physics only).
- Lever
- A rigid bar rotating about a fulcrum, used to multiply force (Physics only).
- Effort
- The force applied to a lever by the user.
Show 3 more key termsShow fewer key terms
- Load
- The force a lever works against — the weight being moved.
- Gear ratio
- The ratio of teeth numbers, setting the ratio of speeds and moments (Physics only).
- Driver / driven gear
- The gear the input turns (driver) and the gear turned by it (driven).
Revise
Common mistakes
Where students most often lose marks in this chapter — and what to do instead.
Mistake: Measuring the distance in M = F d from the end of the bar instead of from the pivot.
The moment depends on distance to the turning point.
Instead: d is always measured from the pivot to the line of action of the force.
Mistake: Using a distance that is not perpendicular to the force.
A slanted force wastes turning effect.
Instead: M = F d uses the perpendicular distance from the pivot to the line of action.
Show 10 more mistakesShow fewer mistakes
Mistake: Quoting moments in newtons or joules.
Moments are neither forces nor energies.
Instead: Moments are in newton-metres (N m).
Mistake: Balancing moments about different pivots.
Each distance must be measured from one chosen pivot.
Instead: Take all distances from the same pivot when applying the principle of moments.
Mistake: Forgetting the weight of a uniform beam acts at its centre.
A uniform beam’s weight has its own moment about an off-centre pivot.
Instead: Treat a uniform beam’s weight as acting at its midpoint.
Mistake: Thinking a lever gives you free energy because it multiplies force.
Force gained is distance lost.
Instead: The effort moves through a proportionally larger distance — energy in equals energy out (at best).
Mistake: Saying meshed gears turn in the same direction.
Teeth push each other oppositely.
Instead: Directly meshed gears rotate in opposite directions; a chain or belt keeps the direction the same.
Mistake: Reversing the gear ratio: making the bigger gear the faster one.
More teeth mean a longer circle to travel.
Instead: Speed ratio = driver teeth ÷ driven teeth: the larger gear turns slower.
Mistake: Expecting the faster gear to have the larger moment.
Speed and moment trade off.
Instead: The slower gear delivers the larger turning moment (moment ratio = driven ÷ driver teeth).
Mistake: Believing a heavier child must sit further out on a see-saw.
Their larger weight already gives a larger moment per metre.
Instead: The heavier child sits closer to the pivot to balance a lighter child further out.
Mistake: Adding moments of forces on opposite sides instead of equating clockwise and anticlockwise sums.
They oppose each other’s rotation.
Instead: Sum each side separately and set the totals equal for balance.
Mistake: Using g to convert to weight when the force is already given in newtons.
Double conversion changes the value.
Instead: If the force is already a weight in N, use it directly in M = F d.
Check yourself
Quick quiz
24 questions with instant explanations. About 5 minutes.
Question 1 of 3
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Define a moment
The moment of a force is its
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Practise
Topical questions
12 exam-style questions with model answers and mark schemes.
A set of structured and calculation questions matched to this chapter, in three tiers, each with a model answer, mark scheme and examiner tip. Higher-tier and Physics-only questions are tagged.
Practise topical questionsExam practice
Practice paper
A 30-mark paper in the style of a GCSE paper, with a separate mark scheme. Give yourself 40 min.
Question paper
Chapter 12 Practice Paper
30 marks · 40 min · 5 pages
10 multiple-choice questions and structured questions with answer lines. Chapter 12: moments M = F d, the principle of moments, levers as force multipliers, and gear ratios for speed and turning moment (Physics only content).
Mark scheme
PROChapter 12 Practice Paper — mark scheme
Answers · Marking points · 3 pages
Model answers with a mark for each creditworthy point — for marking at home or in class.
How is this chapter examined?
Paper 1
1 h 45 · 100 marks
Chapters 1–7: energy, electricity, particle model, atomic structure
Paper 2
1 h 45 · 100 marks
Chapters 8–18: forces, waves, magnetism and electromagnetism, space physics
Tiers
Foundation (grades 1–5) · Higher (grades 4–9)
Higher assumes all Foundation content; the equation sheet is printed
Want a full paper? Try the Paper 1-style (Foundation), Paper 1-style (Higher), Paper 2-style (Foundation), Paper 2-style (Higher), Required practicals practice sets.
Questions
Frequently asked questions
Is this chapter in Combined Science?
No — moments, levers and gears are separate (triple) Physics content on AQA, Edexcel and OCR Gateway. Combined Science students can skip it.
Why does the distance have to be perpendicular?
Only the part of the force’s line of action that sweeps round the pivot creates turning. Pushing along a line through the pivot creates no moment at all, however hard you push.
Do levers create free energy?
Never. A lever that multiplies your force by 15 makes your end of the bar move 15 times further, so the energy you transfer is the same (or slightly more, once friction takes its cut).
Why does the larger gear turn more slowly?
Its teeth are further from the centre, so each turn covers more distance. When the gears mesh tooth-for-tooth, the bigger wheel completes fewer turns in the same time — but pushes with a larger moment.
How do I spot which side is clockwise?
Imagine standing at the pivot looking along the force: a force that would rotate the object the way clock hands move is clockwise. On a see-saw, a weight on the right of the pivot turns the system clockwise.
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No. AQA, Pearson Edexcel and OCR are named only to identify the specifications this content supports. QuizQuip is not affiliated with, endorsed by, or connected to AQA, Pearson Edexcel or OCR, and no past-paper or specimen material is reproduced.
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Chapter 13: Pressure in fluids (Physics only)