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# Power needed to rotate wheels 1 and 2, torque, rotation

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Gears are important components in many mechanical devices, from mechanical clocks to bicycles. In fact, they are present whenever a motor produces rotational motion.

An example of a simple gear system is shown in the figure. (Intro 1 figure) The bigger wheel (wheel 1) has radius r1 , while the smaller one (wheel 2) has radius r2. The two wheels have small teeth and are connected through a metal chain so that when wheel 1 rotates, the chain moves with it and causes wheel 2 to rotate as well.

A) Let wheel 1 rotate at a constant angular speed W. Find the ratio W1/W2 of the angular speed of wheel 1 to the angular speed of wheel 2. Express your answer in terms r1 and r2.

B) The rotation of wheel 1 is caused by a torque T1. Find the ratio r1/r2 of the torque acting on wheel 1 to the torque acting on wheel 2. Express your answer in terms of r1 and r2.

C) If the power needed to rotate wheel 1 is P1, what is the ratio P1/P2 of the power of wheel 1 to the power of wheel 2?