1. The problem statement, all variables and given/known data A length of thread is wrapped many times around a steel disc of mass M and radius R, which is free to rotate around a fixed, frictionless, horizontal axle. The end of the thread is connected to a small object of mass m. If this small mass is held at rest and then released, how fast is it moving after it has fallen through a vertical distance h? Express in terms of M, R, m, g, and h. Make sure this makes sense in extreme limits of M >> m and M << m. 2. Relevant equations V = mgh K_rot = (1/2)Iω^2 V + K = 0 3. The attempt at a solution Energy is conserved, so K = -V. The object has a potential energy at the initial time of m*g*h. This will all be converted into rotational kinetic energy. Therefore, the final rotational energy will be equal to -mgh. (1/2)Iω^2=-mgh The moment of inertia for a disc is (1/2)MR^2. Some basic algebra to isolate the angular velocity gives ω=√(MmghR^2) Am I correct? I guess I was unsure about whether the moment of inertia selected was correct. I also wasn't sure about the extreme conditions. Thanks in advance!