The pulley in the illustration is a uniform disk of mass 2.8 kg and radius 0.24 m, which is free to rotate without friction. The mass of the block is 1.2 kg. Downward and clockwise are negative directions. (a) What is the angular acceleration of the pulley?

Explanation:

Newton's 2nd law, as applied to rotating objects, can be written as

where I = moment of inertia

= for a disk

M = mass of disk/pulley

Since the hanging mass m is the only providing torque on the pulley, we can then write NSL as

Solving for the angular acceleration , we get the expression