The drawing shows the front and rear sprockets of a bicycle. Assume the chain do

Question

The drawing shows the front and rear sprockets of a bicycle. Assume the chain does not slip
or stretch. The radius of the front sprocket is r cm front 10.0 , while that of the rear sprocket
is r cm rear 2.0 . A rider is pedaling the bicycle so that the initial angular speed of the front
sprocket is 5.9 rad/s.

a. What angular acceleration should be applied to the front sprocket to double the angular speed of the rear sprocket?

b. How much time is required to double the speed of the rear sprocket?

Explanation / Answer

Image is missing

Still the distance covered by both the the sprocket must be the same and hence the velocity of bottom most point in the sprocket
=> 1R1= 2R2 => 2 = 59/2 = 29.5 rad/s

When the rear sprocket turns 29.5 rad the front sprocket turns 5.9 rad

So when Front sprocket must complete 0.2 revolution for every one revolaution of rear sprocket

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