A spool of mass ms = 150 kg and inner and outer radii ρ = 0.8 m and R = 1.2 m, respectivel...

A spool of mass ms = 150 kg and inner and outer radii ρ = 0.8 m and R = 1.2 m, respectively, is connected to a counterweight A of mass mA = 50 kg by a pulley system whose cord, at one end, is wound around the inner hub of the spool. The center G of the spool is also the center of mass of the spool, and the radius of gyration of the spool is kG = 1 m. The system is at rest when the counterweight is released, causing the spool to move to the right. Assume that the spool rolls without slip.

Neglecting the inertia of the pulley system, determine the angular speed of the spool after the counterweight has dropped 0.5 m.

Figure P8.46