# Moment of inertia cylinder problem

## Homework Statement

A bucket of water of mass 20 kg is suspended by a rope wrapped around a windlass in the form of a solid cylinder 0.2 m in diameter, also of mass 20 kg. The cylinder is pivoted on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls 20 m to the water. Neglect the weight of the rope.
(a) what is the tension in the rope while the bucket is falling
(b) with what velocity does the bucket strike the water?
(c) What was the time of the fall?
(d) While the bucket is falling, what is the force exerted on the cylinder by the axle?

## Homework Equations

all the basic velocity, initial velocity, etc. equations
I=1/2MR^2
T-Mg=ma

## The Attempt at a Solution

I solved parts A and B easily enough. However, I am not sure if my teacher gave me the wrong answer to C. By using both v=v0+aT and y=y0+v0T+1/2aT^2 I get T=2.47 s, but the correct answer is supposedly around 7 s...

Additionally, I figured that the force of the axle on the cylinder would be the opposing force to the centripetal force ma of the cylinder, but the correct answer is twice this value..

all help would be greatly appreciated