A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius
cylinder at the top of a well. The bucket is raised to the top of the well and released. The bucket is moving
with a speed of 8.0 m/s upon hitting the water surface in the well. What is the angular speed of the cylinder at this instant?
The answer is 39 rad/sec but I am not sure how to get that answer

Question

A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius 
cylinder at the top of a well. The bucket is raised to the top of the well and released. The bucket is moving 
with a speed of 8.0 m/s upon hitting the water surface in the well. What is the angular speed of the cylinder at this instant?
The answer is 39 rad/sec but I am not sure how to get that answer

anonymous · Answer

do you have picture for this problem?

anonymous · Answer

No

anonymous · Answer

sorry I could not understand the problem. is that exactly how it is written?

anonymous · Answer

rope needs to have same speed along its length, that means at the point where rope meets the cylinder the cylinder has same speed, from 
$$v=\omega r$$
$$\omega=v/r=8m/s/0.05m=160rad/s$$

anonymous · Answer

Yeah that's exactly how its written....thanks anyway