What you'll learn
A small force can lift a heavy load if it is applied in the right place — that is the principle behind levers, spanners and gears. For AQA GCSE Physics you need to understand the moment of a force, the principle of moments for a balanced object, and how levers and gears transmit and change the effect of forces. This guide covers the moment equation, the principle of moments and how to use it in calculations, how levers act as force multipliers, and how gears change force and speed. By the end you should be able to calculate moments, apply the principle of moments to balanced systems, and explain how levers and gears work.
Key terms and definitions
Moment — The turning effect of a force about a pivot.
Pivot — The fixed point about which an object turns.
Perpendicular distance — The straight-line distance from the pivot to the line of action of the force, at right angles to it.
Principle of moments — When an object is balanced, the total clockwise moment equals the total anticlockwise moment.
Lever — A rigid object that turns about a pivot to transmit or multiply a force.
Gear — A toothed wheel that transmits turning forces between shafts.
Effort — The force applied to a lever or machine.
Load — The force that a lever or machine moves or overcomes.
Core concepts
The moment of a force
A moment is the turning effect of a force about a pivot. It is calculated using:
moment = force × perpendicular distance from the pivot (M = F × d)
The force is in newtons (N), the distance in metres (m), and the moment in newton metres (N m). The perpendicular distance is measured at right angles from the pivot to the line of action of the force. The further the force is applied from the pivot, the larger the moment, which is why a longer spanner makes it easier to undo a tight bolt.
The principle of moments
When an object is balanced (not turning), the total turning effect one way equals the total turning effect the other way. This is the principle of moments:
total clockwise moment = total anticlockwise moment
This principle is used to solve problems about balanced beams, seesaws and similar systems. If you know the forces and distances on one side, you can find an unknown force or distance on the other side by setting the two moments equal.
Using the principle of moments
To solve a moments problem:
- Identify the pivot.
- Work out the clockwise moment(s): force × distance for each force turning that way.
- Work out the anticlockwise moment(s) in the same way.
- Set the total clockwise moment equal to the total anticlockwise moment.
- Solve for the unknown.
This is a very common calculation, so practise setting it out clearly.
Levers as force multipliers
A lever is a rigid object that turns about a pivot. Levers are useful because they can act as force multipliers: by applying a small effort at a large distance from the pivot, you can move a large load that is close to the pivot. Because the effort acts over a larger distance from the pivot, its moment can balance the larger load's moment even though the effort force is smaller. Examples include a crowbar lifting a heavy object, a spanner, scissors and a wheelbarrow. The longer the distance from the pivot to the effort, the greater the force multiplication.
Gears
Gears are toothed wheels that lock together to transmit the turning effect (moment) of a force from one shaft to another. When two gears of different sizes mesh, they change the moment and the speed of rotation:
- A small gear driving a large gear increases the moment (turning effect) but the large gear turns more slowly.
- A large gear driving a small gear decreases the moment but the small gear turns more quickly.
So gears allow you to trade turning force against speed. This is used in bicycles and vehicles: a low gear gives more turning force for climbing hills but less speed, while a high gear gives more speed but less force. The gears transmit the moment from one wheel to the next, and the ratio of their sizes determines the change.
The centre of mass and balance
Moments also explain why objects balance or topple. The centre of mass is the point where the whole weight of an object seems to act. An object will balance if it is supported directly below its centre of mass, and it will topple if its centre of mass moves outside its base. This is because the weight acting through the centre of mass creates a moment about the edge of the base. A wide base and a low centre of mass make an object more stable, because the centre of mass has to move further before it passes outside the base. This is why racing cars are built low and wide, and why a tall, narrow object tips over easily.
Balancing beams with several forces
More complex moments problems involve several forces acting at different distances from the pivot. To solve these, work out the moment of each force separately (force × its own distance from the pivot), then add up all the clockwise moments and all the anticlockwise moments before setting the two totals equal. The weight of the beam itself may also act at its centre of mass, which you may need to include. Setting the problem out carefully, listing each force and its distance, prevents mistakes and earns method marks even in a multi-step calculation.
Worked examples
Example 1: Calculating a moment
A force of 20 N is applied to a spanner at a perpendicular distance of 0.25 m from the bolt. Calculate the moment. Moment = force × distance = 20 × 0.25 = 5 N m.
Example 2: A balanced seesaw
A child weighing 300 N sits 2 m from the pivot of a seesaw. Where must a 400 N child sit to balance it? Using the principle of moments: clockwise moment = anticlockwise moment. 300 × 2 = 400 × d, so 600 = 400d, giving d = 1.5 m from the pivot.
Example 3: Why a longer spanner helps
Explain why a longer spanner makes it easier to undo a tight bolt. The moment equals force × distance from the pivot. A longer spanner increases the distance, so the same force produces a larger moment (turning effect), making it easier to turn the bolt.
Example 4: Gears changing force and speed
A small gear drives a larger gear. Describe the effect on the turning force and speed. The larger gear turns with a greater moment (more turning force) but rotates more slowly than the small driving gear. Force is increased at the expense of speed.
Common mistakes and how to avoid them
The most common error is using the wrong distance. The moment uses the perpendicular distance from the pivot to the line of action of the force. If the force is at an angle, you must use the perpendicular distance, not the length along the object.
Students often forget to convert distances to metres, or mix up centimetres and metres. Keep the distance in metres so the moment is in newton metres.
In principle-of-moments problems, a frequent mistake is not identifying which moments are clockwise and which are anticlockwise. Sort each force into the correct group before setting them equal.
When explaining gears, do not say a bigger gear is "more powerful". It provides a greater moment (turning force) but turns more slowly — the trade-off is force against speed.
Finally, remember levers multiply force by applying the effort at a greater distance from the pivot than the load. Getting the effort and load distances the wrong way round gives the opposite conclusion.
Exam technique for "Moments, levers and gears"
For calculations, always write M = F × d, keep distances in metres, and for balance problems set total clockwise moment equal to total anticlockwise moment. Show your working clearly to earn method marks.
For levers, explain force multiplication in terms of moments: a small effort at a large distance balances a large load at a small distance. Be ready to give examples such as a crowbar or spanner.
For gears, explain the trade-off between force and speed, and remember that gears transmit the moment from one shaft to another. Use precise terms — moment, pivot, perpendicular distance, effort, load — throughout, and state units (N m) in your answers.
Quick revision summary
- A moment is the turning effect of a force: moment = force × perpendicular distance from the pivot (M = F × d), in N m.
- The principle of moments: for a balanced object, total clockwise moment = total anticlockwise moment.
- A lever multiplies force by applying a small effort far from the pivot to move a large load close to the pivot.
- A longer distance from the pivot gives a larger moment, so a longer spanner makes turning easier.
- Gears transmit the moment between shafts: a small gear driving a large gear increases force but reduces speed, and vice versa.
- Always use the perpendicular distance in metres, and identify clockwise and anticlockwise moments correctly.