Gears are important components in many mechanical devices, from mechanical clock

Question

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. (Figure 1) 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. The rotation of wheel 1 is caused by a torque tau 1. Find the ratio tau 1/tau 2 of the torque acting on wheel 1 to the torque acting on wheel 2. Express your answer in terms of any or all of the variables r1 and r2. 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? Express your answer in terms of any or all of the variables r1 and r2.

Explanation / Answer

part b

conservation of angular momentum

r1 1 = r2 2

r1/r2 = 2/1

1/2 = 1/2 = r2/r1

part c

P = x

p1/p2 = (1/2)x(1/ 2)

= (r2/r1)^2

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