Moments, levers and gears

Physics · Forces. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A force can make an object turn about a pivot. The turning effect of a force is called its moment. It depends on the size of the force and on how far its line of action is from the pivot. The distance must be the perpendicular distance.

If an object is balanced, the total clockwise moment about the pivot equals the total anticlockwise moment. This is the principle of moments.

A lever is a force multiplier: a small effort far from the pivot can move a large load close to the pivot. Gears also pass on turning effects. Their teeth push on each other, so touching gears turn in opposite directions.

Rules to remember

moment = force × perpendicular distance from the pivot to the line of action (M = Fd); unit N m.
Balanced object: total clockwise moment = total anticlockwise moment.
A longer distance from the pivot gives a bigger moment for the same force.
A small gear driving a larger gear: the larger gear turns more slowly but with a larger moment.
A large gear driving a smaller gear: the smaller gear turns faster but with a smaller moment.

Common mistake

Students measure distances from the end of the beam or use the length of the spanner. Always measure the perpendicular distance from the pivot to the line of the force.

Worked example

A 12 N weight hangs 0.25 m to the left of the pivot of a balanced beam. What downward force is needed 0.60 m to the right of the pivot to keep it balanced?

Anticlockwise moment = 12 × 0.25 = 3.0 N m.
For balance, clockwise moment = 3.0 N m, so F × 0.60 = 3.0.
F = 3.0 ÷ 0.60 = 5.0 N.

Answer: 5.0 N

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