Halliday, Resnick & Walker — Rotation: Problem Problem_66

A uniform spherical shell of mass \(M = 4.5 \text{ kg}\) and radius \(R = 8.5 \text{ cm}\) can rotate about a vertical axis on frictionless bearings (Fig. 10.28). A massless cord passes around the equator of the shell, over a pulley of rotational inertia \(I = 3.0 \times 10^{-3} \text{ kg} \cdot \text{m}^2\) and radius \(r = 5.0 \text{ cm}\), and is attached to a small object of mass \(m = 0.60 \text{ kg}\). 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 82 cm after being released from rest? Use energy considerations.