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Hi! I really need help answering this question. I am really bad at Physics and have no idea what I'm doing, so if someone could help me out I would really appreciate it! Thank you!

8. A bucket filled with water has a mass of 23 kg and is attached to a massless rope, which in turn, is wound around a 0.050-m radius cylinder that rotates about a frictionless axle at the top of a well. The bucket is raised to the top of the well and then released to fall back into the well. What is the angular speed of the cylinder at the instant the bucket is moving at 8 m/s?

The answer is 160 rads/s, but how?

(I think)

Torque = Force * radius

Alpha = [omega (final) - omega (initial)]/time

Alpha = linear speed/angular speed

Torque (T) = F (force) * r (radius)

11.5 Nm = (25 kg)(10 m/s^2) * ( .050 m)

I have no idea where to go from here or if it's even relevant to the problem :(

Thanks again in advance.

## Homework Statement

8. A bucket filled with water has a mass of 23 kg and is attached to a massless rope, which in turn, is wound around a 0.050-m radius cylinder that rotates about a frictionless axle at the top of a well. The bucket is raised to the top of the well and then released to fall back into the well. What is the angular speed of the cylinder at the instant the bucket is moving at 8 m/s?

The answer is 160 rads/s, but how?

## Homework Equations

(I think)

Torque = Force * radius

Alpha = [omega (final) - omega (initial)]/time

Alpha = linear speed/angular speed

## The Attempt at a Solution

Torque (T) = F (force) * r (radius)

11.5 Nm = (25 kg)(10 m/s^2) * ( .050 m)

I have no idea where to go from here or if it's even relevant to the problem :(

Thanks again in advance.

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