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Gears are wheels with toothed edges that rotate on an axle or shaft. The teeth of one gear fit into the teeth of another gear. This lets one gear turn the other, meaning one axle or shaft can be used to turn another shaft.

Rotation and transmission of forces by gears

As one gear turns, the other gear must also turn. Where the gears meet, the teeth must both move in the same direction. In the diagram, the teeth of both gears move upwards. This means that the gears rotate in opposite directions.

The forces acting on the teeth are identical for both gears, but their moments are different:

• if a larger gear is driven by a smaller gear, the large gear will rotate slowly but will have a greater moment, eg a low gear on a bike or car
• if a smaller gear is driven by a larger gear, the larger gear will rotate quickly but will have a smaller moment, eg a high gear on a bike or car

Example

A gear with a radius of 0.1 m is turned by a gear with a radius of 0.05 m. The moment of the smaller gear is 20 Nm. Calculate the moment of the larger gear.

First calculate the force on the teeth of the smaller gear:

Use the answer above to calculate the moment of the larger gear:

moment of a force = force × distance

moment = 400 × 0.1

moment = 40 Nm

Turning a gear that has double the radius, doubles the turning effect - it is a 2× force multiplier.