A uniform spherical shell of mass M = 8.00 kg and radius R = 0.550 m can rotate about a vertical axis on frictionless bearings. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.130 kg·m2 and radius r = 0.140 m, and is attached to a small object of mass m = 2.00 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen a distance 1.27 m after being released from rest? Use energy considerations.

Answer 1

set the change of PE of the hanging mass equal to the sum of the KE of the hanging mass, the pulley, and the spherical shell, and solve. Note that you will have to change the angular speed of the pulley, and the shell to tangential velocity (w*r=v) inorder to have a common unknown, v.