The hook, worked
Left: W = 3 × 9.8 = 29.4 N; M = 29.4 × 1.0 = 29.4 N m
Right: W = 2 × 9.8 = 19.6 N; M = 19.6 × 2.5 = 49 N m
49 > 29.4: it turns clockwise, the lighter right side down
Moments, levers and gears Why can a lighter load balance a heavier one?
Foundation and Higher · AQA · 45 minutes
Students predict which way a beam with a heavy load near the pivot and a lighter one far out will turn, then balance a virtual beam themselves by moving a load, the pivot and a mass. Levers and gears follow from the same equation. Slides to present, a vote that shows who's stuck, practice and homework.
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The idea in one minute
A force can turn something about a pivot. Its turning effect, its moment, is the force times the perpendicular distance from the pivot to the force's line of action: M = F d, in newton metres (N m). A load's force is its weight, W = m g, so a mass in kilograms is turned into newtons first (g = 9.8 N/kg). An object is balanced when the total clockwise moment about the pivot equals the total anticlockwise moment. That is why a small force far from the pivot can balance a big one close to it, which is what levers do; gears pass a turning effect from one wheel to the next, and a bigger gear turns more slowly with a bigger moment.
The lesson starts with a prediction before anyone explains: which way will a beam turn when the heavier load is nearer the pivot? Students then balance a virtual beam themselves (an interactive scene, not a substitute for a practical), reading positions from the beam's end and turning them into distances from the pivot each time. It is for Foundation and Higher; the stretch balances three loads, and the gears' moments lean towards Higher.
By the end, students can
- work out a moment with M = F d, in N m, using the distance from the pivot
- turn a mass into a weight with W = m g before working out its moment
- use the principle of moments to find a force or a distance on a balanced object
- explain how levers and gears pass on and multiply the turning effect of a force
Key words
- moment
- pivot
- perpendicular distance
- newton metre (N m)
- clockwise
- anticlockwise
- principle of moments
- lever
- gear
Before this lesson
Students should know that weight = mass × g (W = m g, g = 9.8 N/kg) and rearrange a formula such as M = F d. Forces and weight come first.
Taught in Newton's laws of motion.
The lesson, step by step
45 minutes in total. The stretch is optional.
5 min 1 · Hook · students think
Which way will it turn?
A heavier load near the pivot and a lighter one far out: students vote on which way the beam turns before anyone explains.
Say“A beam on a pivot 1.5 m from its left end. 3 kg sits 1 m to the left of the pivot; 2 kg sits 2.5 m to the right. When I let go, which way does it turn? Left side down, right side down, or does it balance?”
Ask- What would make the right side go down? What would make the left side go down?
- If the 2 kg slid further out, would your answer change?
Watch forSaying the heavier side always goes down, or the further load always wins: keep both answers, the next step needs them.
For the teacher
Give a minute of silent thinking, then vote. Many say the heavier side goes down; some say the load further out wins.
Don't explain yet. Both the mass and the distance matter, and only the product decides: that is the next step. (It turns clockwise, the lighter right side down: 49 N m against 29.4 N m.)
Take a vote with Ask the class: left side down, right side down, or balanced. Keep the votes on the board for the explain step.
Shorter: Vote once, no discussion (−2 min).
12 min 2 · Explain · you explain
Moments, balance, levers and gears
M = F d with the distance from the pivot; weight first; the principle of moments answers the hook; then levers and gears.
Say“A moment is a force times its distance from the pivot. Always from the pivot, and always the weight in newtons, not the mass.”
Ask- This load is 0.5 m from the end of the beam. How far is it from the pivot?
- Which load turns the beam clockwise? Anticlockwise?
- Make the spanner longer. What happens to the force you need?
Watch forTaking the distance from the end of the beam: the slides give positions from the left end on purpose. Ask where the pivot is first.
A lever: force × distance
A nut needs 100 N m to undo
A 0.25 m spanner: F = 100 ÷ 0.25 = 400 N
A 0.50 m spanner: F = 100 ÷ 0.50 = 200 N
For the teacher
Moment: M = F d, force in newtons, d the perpendicular distance from the pivot to the line of the force, in metres; the moment in newton metres, N m. A force through the pivot has no moment.
Distance from the pivot: the slides give positions from the beam's left end, as the virtual beam does. Take the pivot's position away every time. A load's force is its weight, W = m g.
Balanced: the total clockwise moment about the pivot equals the total anticlockwise moment. Work the hook: 29.4 N m anticlockwise against 49 N m clockwise, so the lighter right side goes down. Then ask where the 2 kg would have to sit to balance, and leave it open: the first virtual beam asks the same.
Levers: a spanner, a crowbar, a wheelbarrow. The same moment with a longer distance needs a smaller force: F = M ÷ d. The catch: the end you push moves further than the load does.
Gears: the teeth push each other with the same force where they meet. The bigger gear's teeth are further from its centre, so it gets a bigger moment, and it turns more slowly: 10 teeth driving 30 teeth gives three times the moment at a third of the speed.
Before the spanner slide, ask the class: a spanner twice as long, how much force? Then move a on its graph.
Shorter: Skip the spanner graph and the gears slide; say gears in a line (−4 min).
12 min 3 · Your turn · students write
Balance the beam, then yours
Students balance a virtual beam three ways (move a load, move the pivot, choose a mass), each checked at once, then solve twins of worked examples.
Say“This beam is an interactive scene: a model, not a practical. Predict first, then move it until it balances. Positions are from the beam's left end.”
Ask- Before you move it: which way is it turning, and why?
- Once it balances: how far is each load from the pivot?
Watch forWriting the load's position from the end as its distance from the pivot.
Balance: find a distance
A see-saw: 300 N sits 2.0 m left of the pivot
400 N on the right: 400 × d = 300 × 2.0 = 600
d = 600 ÷ 400 = 1.5 m
Then theirs
250 N sits 1.6 m left of the pivot. Where must 320 N sit on the right?
Mass first: W = m g
1.5 kg hangs 0.40 m from the pivot (g = 9.8 N/kg)
W = 1.5 × 9.8 = 14.7 N
M = 14.7 × 0.40 = 5.88 N m
Then theirs
2.0 kg hangs 0.25 m from the pivot. Its moment?
Positions from the end
Pivot 1.2 m from the left end; 50 N at 0.2 m from it
d = 1.2 − 0.2 = 1.0 m
M = 50 × 1.0 = 50 N m
Then theirs
Pivot 2.5 m from the left end; 40 N at 4.0 m from it. Its moment?
Each beam is an interactive scene (a model, not a practical): the beam is light, g = 9.8 N/kg, and positions are measured from the beam's left end. Predict which way it turns, then move it until it balances.
- The pivot is 2.0 m from the left end. Load 1 (3 kg) is 1.0 m from the left end; load 2 (2 kg) is at 2.5 m. Work out on paper where load 2 must go, then slide it there until the beam balances.They change an interactive scene (moments on a beam) until it does it.
- Now it balances: how far is load 2 from the pivot, in metres?
- Load 1 (6 kg) is 0.5 m from the left end; load 2 (2 kg) is at 3.7 m. Predict: should the pivot move left or right? Then move it until the beam balances.They change an interactive scene (moments on a beam) until it does it.
- Where did the pivot end up, and why there?
- The pivot is 2.0 m from the left end. Load 1 (5 kg) is at 0.4 m, load 2 (2 kg) at 3.0 m and load 3 at 3.5 m. Work out on paper what mass load 3 needs, then set it so the beam balances.They change an interactive scene (moments on a beam) until it does it.
- Load 3 is moved to the right end of the beam, 4.0 m from the left end. What mass, in kg, would it need now to balance? (Work it out; the scene stays as it is.)
For the teacher
The beam in the scene is light (its own weight is left out) and g is 9.8 N/kg. As they move it, each scene says which way the beam turns and the total moment about the pivot, so ask for the answer on paper first: otherwise it is trial and error. Once a beam is checked, its working lists each load's moment.
First beam: slide load 2 until it balances. Second: move the pivot. Third: choose load 3's mass. After each, a question on distances from the pivot, on why it balanced, or on what would balance if a load moved.
Work the examples aloud while the slower ones finish the scenes; the twins check they multiply, turn kilograms into newtons and take distances from the pivot.
Students open the Lab quiz on their own devices; each beam is checked as soon as it balances. Open the answers slide once most have done the twins.
Shorter: Do the first two beams and the first pair only (−4 min).
Longer: Each student sets a beam for a partner to balance, and works it out on paper first (+3 min).
12 min 4 · Who's stuck? · students vote
Vote, then practise
One question shows who takes the distance from the wrong place; then practice in levels, and a beam with three loads as the stretch.
Say“Choose an answer on your own. Nobody talks until everyone has chosen.”
Ask- Where is the pivot? So how far is the force from it?
Watch forMultiplying before the pivot is marked: ask where the pivot is first, then each distance from it.
Show your working on paper. Use g = 9.8 N/kg. Give moments in N m and forces in N; turn centimetres into metres first. The stretch is optional.
The question that shows who's stuck
- A light beam 3.0 m long has its pivot 0.5 m from its left end. A 20 N weight hangs at the right end. What is the weight's moment about the pivot?
In your Classroom, as they answer (an example) - A8
- B9
- C5
- D3
Each wrong answer is a different mistake. While they answer, your Classroom shows who chose which, so you know in seconds whom to help with what.
- A force of 40 N pushes at right angles to a door, 0.50 m from its hinges. What is its moment, in N m?
- A nut is stuck tight. Which push gives the biggest moment?
- A 2.5 kg mass hangs 0.40 m from a pivot. Use g = 9.8 N/kg. What is its moment, in N m?
- A light plank 3.0 m long pivots at its middle. A 30 N weight sits 0.5 m from the left end. What is the weight's moment about the pivot, in N m?
- A force of 12 N acts at right angles 25 cm from a pivot. What is its moment, in N m?
- A child weighing 400 N sits 1.5 m from a see-saw's pivot. How far from the pivot, on the other side, must a child weighing 300 N sit to balance, in metres?
- A small gear with 10 teeth turns a large gear with 30 teeth. Compared with the small gear, the large gear turns…
- With a long crowbar, a small push lifts a heavy stone. What is the catch?
- A crowbar's pivot is 0.10 m from a 600 N stone, and you push 1.2 m from the pivot on the other side. What push, in newtons, just balances the stone?
- A light beam pivots at its middle. On the left, 20 N hangs 1.0 m from the pivot and 10 N hangs 0.5 m from it. How far to the right of the pivot must a 25 N weight hang to balance, in metres?
- Stretch: the pivot is 2.0 m from the left end, 4 kg sits at 0.5 m and 1 kg at 3.0 m. Choose load 3's mass and place so the beam balances. Then find a second way on paper.They change an interactive scene (moments on a beam) until it does it.
Support · Draw the beam, mark the pivot, and write each distance from the pivot on the drawing before any multiplying. For balance: clockwise moments on one side of an equals sign, anticlockwise on the other.
For the teacher
Everyone chooses before anyone explains. Then ask in turn: where is the pivot? How far is the weight from it? What is the force times that distance?
Questions 1–3 build fluency; 4–5 change the look (positions from the end, centimetres); 6–8 ask for reasons; 9–10 are exam-style. The stretch balances a virtual beam with three loads, more than one way.
Students show their working on paper or the board; the quiz keeps their final answers.
If many chose an answer from the wrong distance, draw the beam with a ruler under it and mark the pivot, before they practise.
Shorter: After the vote, questions 1–5 only (−5 min).
Longer: The stretch: balance three loads two different ways (+8 min).
4 min 5 · Exit · students show
Balance the beam
A balance with positions from the beam's end shows who takes distances from the pivot.
Say“Mark the pivot first, then each distance from it.”
Watch forUsing 4.0 m or 1.0 m for the right-hand distance.
Mark the pivot on a sketch and write each distance from it first.
- A light beam 4.0 m long pivots 1.0 m from its left end. A 600 N load hangs at the left end. What force, in newtons, at the right end balances it?
- The load moves 0.5 m nearer the pivot. What force at the right end balances it now, in newtons?
For the teacher
A light beam 4.0 m long pivots 1.0 m from its left end. A 600 N load hangs at the left end.
What force at the right end balances it? And if the load moved 0.5 m nearer the pivot?
Those who used a distance from the end need it again next lesson; set the homework.
Longer: Why is a door handle put far from the hinges? Answer with a moment. (+4 min).
One to one: before any calculation, ask the student to point to the pivot and say each distance from it aloud, and to say which way each load turns the beam; let them drive the virtual beam while you only ask what they predict before each move.
Homework: Moments, levers and gears
Use g = 9.8 N/kg. Draw a sketch for each question with the pivot marked and each distance from it written on.
- A force of 25 N acts at right angles 0.60 m from a pivot. Find its moment.
- A 4.0 kg mass hangs 0.75 m from a pivot. Find its weight, then its moment.
- A 450 N adult sits 1.2 m from a see-saw's pivot. Where must a 360 N child sit to balance?
- A light beam 2.0 m long pivots 0.5 m from its left end, with 80 N hanging at the left end. What force at the right end balances it? Give it to 3 significant figures.
- A gear with 12 teeth, turned with a moment of 1.5 N m, drives a gear with 36 teeth. Which turns faster? What moment does the larger gear get?
- Explain, with the idea of a moment, why door handles are put on the side far from the hinges.
Print the worksheet with working space and homework. Teacher answers come with your Library copy.
Teaching moments, levers and gears: common questions
Is moments on Foundation and Higher, and in combined science?
In AQA GCSE Physics (8463) moments, levers and gears is for both tiers, and it is in separate physics only: AQA's combined science does not have it. The whole lesson suits both tiers; the stretch with three loads and the gears' moments lean towards Higher.
Should students use g = 9.8 N/kg or 10 N/kg?
Use what the question gives. AQA gives the value of g in any calculation, usually 9.8 N/kg, and the lesson uses 9.8 throughout, as does the virtual beam. Many exam questions give the weight in newtons already, so there is nothing to turn into newtons.
Why does the virtual beam give positions from the end, not from the pivot?
On purpose: taking a distance from the end of the beam instead of from the pivot is the most common mistake in moments questions, and exam diagrams often give positions that way. Turning each position into a distance from the pivot every time is the habit the lesson builds.
What does perpendicular distance mean here?
The shortest distance from the pivot to the line the force acts along, which meets that line at a right angle. For a weight hanging from a horizontal beam it is the distance along the beam. A force pushing along a spanner, through the nut, has no perpendicular distance from it and so no moment.
How much do students need to know about gears?
AQA asks students to explain how levers and gears pass on the turning effect of a force. For gears: the teeth of two gears push on each other with equal forces, so the gear with the bigger radius (more teeth) gets the bigger moment and turns more slowly. Working out the moment from the number of teeth, as in the homework, is a good extension.
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Yes. Read the lesson, print the worksheet and open its slides without signing in; nothing you draw there is kept. A free teacher account keeps the whole lesson in your Library to change and teach, with the interactive beams, the quizzes, the answers and the answer slides.
Curriculum reference: AQA GCSE Physics 8463: 4.5.4 (moments, levers and gears: M = F d, the principle of moments for a balanced object, levers and gears transmitting the rotational effects of forces; physics only), with 4.5.1.3 (gravity: weight, W = m g).
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