A pulley of moment of inertia I and radius r is fixed to a wall. A rope is wrapped around it and tied to a block of mass m. The block is initially held at rest, and then it is released. The block drops a distance h. The rope does not slip on the pulley, and the magnitude of the acceleration due to gravity is g. You know I, r, m, h, and g. [NOTE: a diagram wasn't given, but the professor said it was just a simple pulley attached to the wall with a block hanging off of it from a rope).
-What is the work done by gravity on the system?
-What is the change in potential energy of the system? change in kinetic energy of the system?
-What is the speed v of the block in terms of I, r, m, h, and g?
-What is the angular speed (omega) in terms of I, r, m, h, and g?
These weren't given in the problem, but:
K = (1/2)*I*w^2 + (1/2)*M*v^2
U = mgy
The Attempt at a Solution
Okay, I have no idea about questions 1 and 3, I think it has something to do with conservation of energy? For question number 2, I had:
K1 + U1 = K2 + U2
But the problem is since the whole system starts out at rest, wouldn't there be no initial energy except for potential? Meaning the "change" in potential energy would only be mgh? Or does the block somehow add potential energy as well?
Thanks in advance, I'm quite at a loss right now and my physics textbook isn't helping :(