If the driver gear has 10 teeth and is moving at 10 RPMs (revolutions per minute), at what speed would the driven gear move if it has 20 teeth?

The speed at which the driven gear moves can be calculated by understanding the relationship between the teeth of the driver gear and the driven gear. This is often called the gear ratio.

The gear ratio is calculated by dividing the number of teeth on the driven gear by the number of teeth on the driver gear.

Now, let's calculate the gear ratio for your gears: Driven gear teeth / Driver gear teeth = 20 teeth / 10 teeth = 2

This means that for every one rotation of the driver gear, the driven gear will rotate half as many times because it has twice as many teeth.

Since the driver gear is moving at 10 RPM, we can now find out how many revolutions per minute the driven gear will make by dividing the driver gear's RPM by the gear ratio.

Driver gear RPM / Gear ratio = 10 RPM / 2 = 5 RPM

So the driven gear would move at 5 revolutions per minute (RPM).

Extra: Gears are a fundamental component of many mechanical systems. They are used to change the speed, torque (rotational force), and direction of a power source. The teeth on the gears interlock so that when one gear (the driver gear) turns, it turns the other gear (the driven gear).

The size and number of teeth on the gears determine how they interact. If a gear has more teeth than another, it will turn more slowly but with more torque. Conversely, if a gear has fewer teeth, it will turn more quickly but with less torque.

The gear ratio, the ratio of the number of teeth on two meshing gears, directly affects the output speed and torque. In your example, the gear with fewer teeth (the driver gear) would cause the gear with more teeth (the driven gear) to rotate more slowly, but it would increase the torque that the driven gear can exert because the force is distributed among more teeth.

Understanding gear ratios is essential in engineering and mechanical design, where gears are used to create efficient and effective machines. Gears can be found in many everyday devices, from clocks to cars to wind turbines.