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A gear consists of a rotating part with teeth or cogs that are used to mesh with other gears in order to transmit torque. Gears are useful for changing the speed, torque and direction of the source of power. Most gears rotate, however linear motion can be achieved using rack and pinion gears. 

Gears are similar to pulleys, however the interlocking teeth provide a greater mechanical advantage as their is no slippage.

When gears with different number of teeth are meshed together, the gear with less teeth will spin faster; although the gear with more teeth spins slower, it will produce proportionally more torque. This relationship is used to generate a mechanical advantage when designing geared machines.

The gear ratio refers to relationship between the angular velocity of the driving gear to that of the driven gear. For simple rotating gears meshed together, the gear ratio can be calculated as follows:

Gear ratio = Number of teeth on driving gear
                    Number of teeth on driven gear

Below are some examples of gears used in angle grinders and lathes.

Gears from an angle grinder  
Gears used to drive a lathe