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Question

A bucket is being lowered down into a well through a rope passing over a fixed pulley of radius 10 cm. Assume that the rope does not slip on the pulley. Find the angular velocity of the pulley at an instant when the bucket is going down at a speed of 20 cm/s and has an acceleration of 4.0 m/s2
  1. 2 rad/s
  2. 20 rad/s 
  3. 0.2 rad/s
  4. 0.02 rad/s


Solution

The correct option is A 2 rad/s
Since the rope does not slip on the pulley, the linear speed v  of the point of contact on pulley is same as the speed of the bucket.

The angular velocity of the pulley is then given by 

ω=vr=20 cm/s10 cm=2 rad/s

Hence option A is the correct answer.
 

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