Consider an aluminum disk with radius of 63.2 mm. The mass of the disk is 464 grams.
The disk is allowed to rotate on a frictionless surface with the rotation axis at its center. The disk has a small pulley rigidly mounted at the top concentrically. The pulley's radius is 12.3 mm, and the mass of the pulley is negligible. A string is wrapped around the pulley, and a hanging mass of 21.8 g is tied at the other end of the string. When the mass falls under gravity, it causes the aluminum annular disk to rotate. Ignore the string's mass, and assume that the string's motion is frictionless.
HINT1: Draw a diagram of your problem first. The hardest part of this problem is not to mix various variables (radii for example) and understanding what radius determines the disk's moment of inertia, which radius determines the torque, and how different radii are related to the amount of the fallen distance.
HINT2: You can either use the conservation of energy or rotational dynamics. The best is to try both and see if they yield the same results.
What is the angular speed of the aluminum disk when the mass has fallen 11.3 cm?
= rad/s