Moments, levers and gears (physics only) — AQA GCSE Physics
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Moments, levers and gears (physics only) explained
A force makes an object turn when its line of action does not pass through the pivot.
Read the full explanation
Push a door at the handle and it swings; push it exactly on the line running through the hinges and it will not turn at all, however hard you push. The further from the pivot the force acts, and the closer to a right angle it is applied, the bigger the turning effect. Two forces can also produce rotation with no overall push: the two hands on a steering wheel, or a force at each end of a spanner, act in opposite directions on opposite sides of the pivot, so they turn the object while the resultant force stays zero. That is why a system of forces, and not only a single force, is named here.
Students should be able to describe examples in which forces cause rotation.
Good answers here name three things: the pivot, the force, and the distance between them. A spanner turns a nut, with the pivot at the centre of the nut, the force from the hand at the end of the handle, and a longer handle giving a larger turning effect for the same force. A door turns about its hinges, which is why the handle is fitted at the far edge. A seesaw turns about its central pivot, and the child sitting further out wins. A wheelbarrow pivots about the wheel axle, so a load placed close to the wheel is easier to lift. Pedals turn a bicycle crank about the axle, and a tap handle turns about the spindle - both made deliberately wide so that a small hand force gives a large moment.
The turning effect of a force is called the moment of the force. The size of the moment is defined by the equation: moment o f a f orce = f orce × distance M = F d moment of a force, M, in newton-metres, Nm force, F, in newtons, N distance, d, is the perpendicular distance from the pivot to the line of action of the force, in metres, m.
A moment is the turning effect of a force, and the equation puts a number on it: the force in newtons multiplied by the perpendicular distance in metres from the pivot to the line of action of the force, giving newton-metres. Perpendicular is the word that earns and loses marks. If the force is applied at an angle, the distance to use is the shortest distance from the pivot to the line the force acts along, not the length of the handle, which is why the same force produces its largest moment when applied at right angles. A 40 N push acting 0.30 m from a pivot gives a moment of 12 N m. The unit looks like an energy, but a moment is a turning effect and is never written in joules.
If an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot.
Balanced means the beam is not turning, requiring the sum of every clockwise turning effect about the pivot to match the sum of every anticlockwise one. Each moment is worked out separately as force multiplied by perpendicular distance and then added to its own side. On a number balance, a 2-unit weight hung at position 3 on the right gives a clockwise moment of 6 units. To balance this, 6 units of anticlockwise moment must be restored on the left, for example by hanging one 1-unit weight at position 6, or one 2-unit weight at position 3. If the two totals are not equal there is a resultant moment and the beam turns the way the larger one points. The pivot supplies whatever upward force is needed to balance the downward forces.
Students should be able to calculate the size of a force, or its distance from a pivot, acting on an object that is balanced.
When a beam balances, the product of force and distance on one side equals the product on the other, and any one of the four quantities can be found if the other three are known. A 4.0 N weight hung 0.60 m to the left of a pivot gives 2.4 N m anticlockwise, so a weight 0.30 m to the right must be 8.0 N. Distances can stay in centimetres provided both sides use centimetres, because the units cancel; the moment itself is only in newton-metres if the distance is in metres. Where several loads act, total each side first and then rearrange. Always sense-check the answer, because the load nearer the pivot must be the larger force.
A simple lever and a simple gear system can both be used to transmit the rotational effects of forces.
A lever and a gear train both take a turning effect in at one place and deliver it at another, usually with a different size of force. A lever is a rigid bar turning about a pivot: because the moments on the two sides must match, a small effort a long way from the pivot balances a large load close to it, so a crowbar, a wheelbarrow and a pair of scissors all multiply force. The price is distance, since the effort end moves much further than the load end. Gears do the same job between two shafts. Their teeth mesh so that neither slips and the wheels turn in opposite directions, and the moment delivered depends on the size of the gear the force finally acts on. Neither device creates energy; both trade force against distance or speed.
Students should be able to explain how levers and gears transmit the rotational effects of forces.
An explanation needs the mechanism, not just the name. For a lever, the moment of the effort about the pivot equals the moment of the load, so effort multiplied by its distance equals load multiplied by its distance; making the effort distance ten times the load distance lets the effort be a tenth of the load. For gears, the force at the meshing teeth is the same on both wheels, so the moment each one carries is that force multiplied by its own radius. A small gear driving a large one therefore delivers a larger moment, but the large gear turns more slowly and through a smaller angle, which is exactly the low gear a cyclist selects for a hill. Swap them and you get speed instead of turning effect. Meshed gears always rotate in opposite directions.
Your focus
- Identify the pivot and the line of action of a force in a diagram of a turning object.
- Explain why a force directed through the pivot produces no rotation.
- Describe two forces acting on opposite sides of a pivot that turn an object without a resultant force.
Show all 21 objectives
- Describe three everyday examples of rotation, naming the pivot in each.
- Explain why a door handle is fitted at the edge furthest from the hinges.
- Predict how lengthening a spanner changes the turning effect for the same force.
- Calculate the moment of a force from a force in newtons and a perpendicular distance in metres.
- Explain why a force applied at right angles to a lever gives the largest moment.
- Identify the perpendicular distance in a diagram where the force acts at an angle.
- Apply the principle of moments to decide whether a loaded beam balances.
- Calculate the total moment on each side of a pivot when two loads hang on one side.
- Predict the direction of rotation when the clockwise and anticlockwise totals differ.
- Calculate an unknown force on a balanced beam from three known quantities.
- Calculate the distance from a pivot at which a given weight balances a beam.
- Check a moments answer by confirming that the nearer load carries the larger force.
- Explain how a lever multiplies force using the principle of moments.
- Describe how meshed gears transmit a turning effect between two shafts.
- Justify why a force multiplier cannot increase the energy transferred.
- Explain the force multiplication of a lever in terms of equal moments about the pivot.
- Compare the moment and the rotational speed of a small gear driving a large one.
- Select the gear arrangement that gives the greater turning effect and justify the choice.
Moments, levers and gears (physics only) exam tips
Marking Points
- one mark for the force acting at a distance from the pivot, so its line of action misses the pivot
- one mark for stating that a force whose line of action passes through the pivot causes no rotation
- one mark for a correct everyday example of a force causing rotation
- one mark for recognising that two opposing forces either side of a pivot can turn an object with no resultant force
- one mark for naming the pivot in the example described
- one mark for naming the force applied and where it acts
- one mark for the perpendicular distance between the pivot and the line of action
- one mark for explaining the turning effect in terms of that force and that distance
- one mark for the moment described as the turning effect of a force
- one mark for the equation moment = force × distance
- one mark for the distance taken perpendicular from the pivot to the line of action of the force
- one mark for the answer in newton-metres
- one mark for stating the total clockwise moment equals the total anticlockwise moment
- one mark for each moment worked out as force × perpendicular distance from the pivot
- one mark for summing all the moments on each side before comparing them
- one mark for stating the direction of the resultant moment where the totals differ
- one mark for setting the total clockwise moment equal to the total anticlockwise moment
- one mark for a correct substitution with matching distance units on both sides
- one mark for rearranging to make the unknown force or distance the subject
- one mark for the answer with the correct unit, newtons or metres
- one mark for a lever described as a rigid bar turning about a pivot
- one mark for a small effort at a large distance balancing a large load at a small distance
- one mark for gears transmitting the turning effect between shafts through meshed teeth
- one mark for stating that the energy transferred is not increased, so force is gained at the cost of distance or speed
- one mark for the moments of effort and load about the pivot being equal for a lever
- one mark for the same force acting at the meshing teeth of both gears
- one mark for the moment on each gear given by that force multiplied by the gear's radius
- one mark for a larger gear turning more slowly while carrying a larger moment
Examiner Tips
- 💡Find the pivot before anything else; the geometry of the whole question follows from it.
- 💡Push at right angles and as far from the pivot as possible is the standard way to maximise a turning effect.
- 💡Structure every answer as pivot, force, distance - three sentences for three marks.
- 💡If asked how to turn something more easily, change the distance rather than the force.
- 💡Write perpendicular distance from the pivot into any definition answer.
- 💡Convert centimetres into metres before multiplying, or the moment comes out a hundred times too big.
- 💡Tabulate the force and the distance for every load before writing the balance equation.
- 💡State which way the beam turns when the moments are unequal; it is usually a mark on its own.
- 💡Write the moment equation out in full before rearranging; the equation itself is a mark.
- 💡Sense-check the result: the closer a load sits to the pivot, the larger its force must be.
- 💡Every lever answer needs the pivot, the effort, the load and the two distances.
- 💡State the trade-off - more force, less movement - because it separates good answers from vague ones.
- 💡Say the same force acts at the teeth; it is the step most answers miss.
- 💡Link large gear to large moment and slow rotation in a single sentence.
Common Mistakes
- assuming any force on an object makes it rotate, whatever its line of action
- measuring the distance from the pivot along the force itself rather than perpendicular to its line of action
- saying a bigger force always gives a bigger turning effect without mentioning the distance
- treating rotation as impossible unless there is a resultant force
- describing the object turning without ever naming the pivot
- placing the pivot at the point where the force is applied
- saying a longer spanner increases the force rather than the moment
- offering an example such as a falling ball in which nothing rotates
- using the length of the spanner or lever when the force is applied at an angle to it
- giving the moment in joules because the unit is the newton-metre
- measuring the distance from the end of the object rather than from the pivot
- answering increase the length of the lever when asked how to increase the moment, which mark schemes refuse; the credited answer is to apply the force further from the pivot
- adding forces instead of moments when more than one weight hangs on the same side
- measuring distances from the end of the beam rather than from the pivot
- assuming a balanced beam needs equal weights, ignoring their distances from the pivot
- leaving out the moment of a second load on one side
- mixing centimetres on one side of the equation with metres on the other
- multiplying where a division is needed in the rearrangement, giving an answer far too large
- measuring the distance from the load to the end of the beam instead of to the pivot
- producing an answer in which the load nearer the pivot is the smaller force
- saying a lever or a gear makes more energy or increases the work done
- forgetting that meshed gears turn in opposite directions
- describing a lever without identifying its pivot
- claiming a longer lever increases the weight of the load rather than the moment available
- stating that the larger gear turns faster because it is bigger
- saying gears change the force at the teeth rather than the moment about each axle
- describing the low gear on a bicycle as the one that gives more speed
- omitting the reversal of rotation direction between meshed gears