Halliday, Resnick & Walker — Rotation: Problem 66

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. 10-38). 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 \( 82 \text{ cm} \) after being released from rest? Use energy considerations.