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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. For example, a low gear on a bike or car.
• If a smaller gear is driven by a larger gear, the smaller gear will rotate quickly but will have a smaller moment. For example, 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.

Rearrange M = F d to find F:

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

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

Reducing unwanted energy transfer

Any surfaces in contact in a machine will dissipate energy through friction. This can be reduced using lubrication so that the machine transfers energy more efficiently and there is less wear on the moving parts.

Contacting machine parts can be lubricated by adding an oily or greasy liquid that holds the surfaces apart a little, and allows them to slide past each other with less friction between them, as with oil in a car engine, for example.