A uniform spherical shell of mass M = 4.5 kg and radius R = 8.5 cm can rotate about a vertical axis on frictionless bearings, see Fig. 1. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 3 × 10−3 kgm2 and radius r = 5 cm, and is attached to a small object of mass m = 0.6 kg. There is no friction on the pulley’s axle; the cord does not slip on the pulley.
1. What is the acceleration of the system?
2. What is the speed of the object when it has fallen 82 cm after being released from rest.