Moments, levers and gears
Moment of a force
A moment is the turning effect of a force about a pivot.
moment = force × perpendicular distance from the pivot
- Symbol: M (or τ).
- Units: newton metres (Nm).
- The distance must be perpendicular to the line of action of the force.
A larger force or a longer perpendicular distance gives a bigger turning effect — that is why a long spanner undoes a tight nut more easily than a short one.
Principle of moments
For an object that is balanced (in rotational equilibrium):
sum of clockwise moments = sum of anticlockwise moments
Use this to solve seesaw, balance-beam and lever problems.
✦Worked example— Worked example — balanced beam
A 2 m uniform beam is pivoted at its centre. A 30 N weight hangs 0.8 m to the left of the pivot. How far to the right must a 24 N weight be placed to balance the beam?
- Anticlockwise moment = 30 × 0.8 = 24 Nm.
- For balance, clockwise moment = 24 Nm.
- 24 = 24 × d → d = 1.0 m to the right.
Levers
A lever is a simple machine that uses a moment to amplify force. A force multiplier has the load close to the pivot and the effort far away (e.g. wheelbarrow, bottle opener, scissors). Edexcel commonly tests the language: "the lever multiplies the input force because the effort acts at a greater distance from the pivot than the load."
Gears
A gear is a wheel with teeth. Two meshed gears rotate in opposite directions; the teeth must match.
- Larger gear meshing with smaller gear → the larger gear turns more slowly but with a larger moment (force multiplier).
- Smaller gear driving larger gear → speeds up and reduces moment.
This is why low gears on a bike (small chainring, large rear cog) make hill-climbing easier — bigger turning force at the wheel.
Edexcel exam tip
Always state units (Nm) and check that distances are in metres before multiplying. Distances given in cm are the most common dropped-mark trap on moments questions.
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