Gears are important components in many mechanical devices, from mechanical clock
ID: 1474807 • Letter: G
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 r_1, while the smaller one (wheel 2) has radius r_2. 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.
Part A
Let wheel 1 rotate at a constant angular speed _1. Find the ratio (_1)/(_2) of the angular speed of wheel 1 to the angular speed of wheel 2.
Express your answer in terms of any or all of the variables r_1 and r_2.
(_1)/(_2) = ______________
Part B
The rotation of wheel 1 is caused by a torque _1. Find the ratio (_1)/(_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 r_1 and r_2.
(_1)/(_2) = ______________Explanation / Answer
since the two wheels are connected,then the linear speeds are equal
V = R*w
for the large wheel V1 = r1*w1
for the smaller wheel v2 = r2*w2
since v1 = v2
r1*w1 = r2*w2
w1/w2 = r2/r1
B) torque 1 = r1*F1
torque 2 = r2*F2
by newton's third law of motion F1 = F2
then (_1)/(_2) = r1/r2
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