A bucket of mass 5 kg is suspended over a well shaft by a winch and a rope. The winch is a solid cylinder of mass M=12 kg and radius R=10 cm that rotates without friction. The bucket must descend a height h=10 meters to reach the water. The moment of inertia of the winch is I = ½ MR2. Ignore the mass of the rope.
(A) What is the speed of the bucket just before it hits the water? Assume that the rope rolls off of the winch without slipping.
(B) What is the angular velocity of the winch just before the bucket hits the water?
(C) What is the rotational kinetic energy of the winch just before the bucket hits the water?