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.

Assume that the inertia of the cord and of pulleys B and D can be neglected, but model pulley C as a uniform disk of mass mC = 15 kg and radius rC = 0.3 m. If the cord does not slip relative to pulley C, determine the angular speed of the spool after A drops 0.5 m.

Figure P8.47