Gear speed can be summarised by the following equation where: =number of teeth on a gear ω=angular velocity	Gear trains change speed and force Gear trains can be used to drastically change the rate at which something rotates. As can be seen from the video above of a 90,000,000,000:1 gear box with an input of 200 rpm the final gear will rotate once every million years.
Gear profiles are essential The most significant development within gearing from their early designs in ancient times is the understanding of involute properties. As can be seen from the figure below in order to achieve uniform motion the involute curves for both gears have to traced out by point g simultaneously.

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