GCSE · Physics · Edexcel · Spec 1PH0

Levers and gears

How can you lift a slab far heavier than your push? Don't push harder. Push further from the pivot.

Balance the lever

How far out does each push need to be?

A 600 N load sits 0.5 m from the pivot on one side of a lever. On the other side, you push down at right angles to the lever (ignore the lever's own weight). For each push below, slide it to the distance from the pivot where it would exactly balance the load. The line is the lever arm on the push side: 0 is the pivot.

Place 600 NPlace 300 NPlace 200 NPlace 150 NPlace 100 N

Worked example: finding an unknown force

Problem

A worker pushes down on one end of a lever with an effort of 150 N, at right angles to the lever, 1.2 m from the pivot. The load sits on the other side, 0.15 m from the pivot. What is the largest load force this effort can balance?

Two ways to use a lever

Force multipliervsDistance multiplier

Look at where the effort and the load sit. That one choice decides what the lever does for you.

Focus

Where the effort acts

Force multiplier

A long way from the pivot

Distance multiplier

Close to the pivot

The insight

This is the difference that decides everything else in the table.

Where the load acts

Force multiplier

Close to the pivot

Distance multiplier

Further from the pivot

What gets bigger

Force multiplier

The force: the load force is larger than the effort

Distance multiplier

The distance: the load end moves further than the effort

What you give up

Force multiplier

The heavy load only moves a small distance

Distance multiplier

The force on the load is smaller than the effort

Example

Force multiplier

A crowbar lifting a heavy object

Distance multiplier

Your lower arm, with the elbow as the pivot

Gears and rotations

Turn one gear, count the other

30-tooth gear turned: 2/6. 30-tooth gear 1/3 turn. Teeth passed 10. 10-tooth gear 1.0 turns

30-tooth gear1/3 turnTeeth passed1010-tooth gear1.0 turns

Gears are toothed wheels that turn about a central axle. Here a 30-tooth gear meshes with a 10-tooth gear. Drag to turn the 30-tooth gear and watch the teeth being passed across. Every time 10 teeth have gone by, the 10-tooth gear has made one complete turn.

Watch out: The two gears do not turn the same number of times. The number of rotations depends on the numbers of teeth: one turn of the 30-tooth gear drives the 10-tooth gear round three times.

Gears and moments

Reason it through

Why can a pair of gears pass a bigger turning effect on to the second gear?

Link 1 of 4

First link · your turn

The first gear is turned by its axle. What does it do to the gear it meshes with?

Locked — reveal the link above first

What do you really think?

What decides the size of a turning effect?

You have now seen levers balance and gears pass a turning effect on. Before you move on, be honest about which of these ideas sounds most right to you.

Which is closest to what you think right now?

The bigger force always gives the bigger turning effect.The distance to use is how far along the lever the force is applied, whichever way the force points.The smaller gear gets the bigger moment, because it spins round more times.It depends on the force and on the perpendicular distance from the pivot to the line of the force.

How sure are you?

I'm sureI think soI'm guessing

The bigger force always gives the bigger turning effect.

This is a common misconception

Force is only half the story. The moment is force × distance, so 100 N acting 3 m from the pivot turns just as hard as 600 N acting 0.5 m away: both are 300 N m. That's exactly why a small effort can balance a heavy load.

The distance to use is how far along the lever the force is applied, whichever way the force points.

This is a common misconception

That only works when the force pushes at right angles to the lever. The distance in M = Fd is the perpendicular distance from the pivot to the line of action of the force. If the force pushes at a slant, draw its line, then measure straight across from the pivot to that line at right angles. That distance is shorter than the distance along the lever, so the moment is smaller.

The smaller gear gets the bigger moment, because it spins round more times.

This is a common misconception

Turning more times is not the same as turning harder. The force at the teeth is the same size on both gears, so each moment is that force × the gear's radius. The gear with the larger radius gets the larger moment.

It depends on the force and on the perpendicular distance from the pivot to the line of the force.

This matches the evidence

Yes. Moment = force × perpendicular distance from the pivot. That one rule explains a balanced lever, a force multiplier, and why the larger gear gets the larger moment.

A turning effect is never just a force. It's force × perpendicular distance from the pivot, on a lever or on a gear.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

moment = force × distance

Where you push matters as much as how hard you push.

What you need to know

A moment is the turning effect of a force, measured in newton metres (N m).
moment = force × distance (M = Fd), where d is the perpendicular distance from the pivot to the line of action of the force.
A balanced lever has equal moments on each side, so an unknown force = moment ÷ distance.
Levers can be force multipliers or distance multipliers, depending on where the effort and load sit.
Interlocking gears pass a moment on: the numbers of teeth set the rotations, and the larger radius gets the larger moment.

The big picture

A force can make something turn, and that turning effect is called a moment: moment = force × perpendicular distance from the pivot, measured in newton metres. A lever balances when the moments on each side are equal, so a small force far from the pivot can balance a large force close to it. Levers can act as force multipliers or distance multipliers. Interlocking gears pass a turning effect from one axle to another: the numbers of teeth decide how many times each gear turns, and because the force at the teeth is the same on both gears, the gear with the larger radius gets the larger moment.

Key points

1A moment is the turning effect of a force. Unit: newton metre (N m).

2Moment = force × distance (M = Fd). The distance is measured perpendicular to the force, from the pivot to the force's line of action.

3A lever rotates about a pivot: an effort force on one end produces a load force on the other.

4On a balanced lever the moments on each side are equal, so a missing force = moment ÷ distance.

5Force multiplier (e.g. a crowbar): effort far from the pivot, load close. The load force is bigger, but the load moves only a small distance.

6Distance multiplier (e.g. the lower arm, elbow as pivot): effort close to the pivot, load further away. The load moves further, but with a smaller force.

7Interlocking gears transmit forces and moments. The numbers of teeth decide the rotations: a 10-tooth gear turns three times for each turn of a 30-tooth gear.

8The force at the teeth is the same size on both gears (Newton's third law), so the gear with the larger radius has the larger moment. Gears can increase a moment.

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Worked example

Problem

A small driving gear of radius 0.05 m is turned with a moment of 2 N m. It meshes with a larger gear of radius 0.15 m. Calculate the moment on the larger gear.

⚠ Watch out

Using the distance along the lever when the force pushes at a slant. The distance in M = Fd is the perpendicular distance from the pivot to the line of action of the force, not just how far along the lever the force is applied.

🧠

Memory hook

Long arm, light push: the moment is force × distance, so what you lose in force you make up in distance.

✓

Check yourself

A 250 N load sits 0.4 m from a pivot. Where must a 50 N effort push, at right angles, to balance it? Which moment do you work out first?

Flashcards

(14)

What is a moment?

The turning effect of a force.

What is the unit of a moment?

The newton metre (N m).

Write the equation for a moment.

moment = force × distance (M = Fd), with force in N and distance in m.

Which distance do you use in M = Fd?

The perpendicular distance from the pivot to the line of action of the force.

What does a lever rotate around?

A pivot.

On a lever, what does the effort force produce?

A load force on the other end of the lever.

When a lever is balanced, what is equal on each side?

The moments (not the forces).

How do you find an unknown force on a balanced lever?

Find the moment on the known side, then force = moment ÷ distance.

A crowbar is a force multiplier. Where do the effort and the load sit?

Effort a long way from the pivot, load close to it. The load force is bigger but moves only a small distance (e.g. a crowbar).

Your lower arm is a distance multiplier. Where do the effort and the load sit?

Effort close to the pivot, load further away. The load moves further but with a smaller force (e.g. the lower arm, elbow as pivot).

What are gears?

Toothed wheels that rotate about a central axle. Interlocking gears transmit forces and transfer moments.

A 30-tooth gear turns once. How many times does a meshing 10-tooth gear turn?

Three times. The number of rotations depends on the numbers of teeth.

How does the force at the teeth compare on two meshing gears?

It is the same size on both, in opposite directions (Newton's third law).

Which of two meshing gears has the larger moment?

The one with the larger radius, because moment = the same tooth force × a larger distance.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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How far out does each push need to be?

What decides the size of a turning effect?

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