The spool of mass m, radius of gyration kG, inner radius ri, and outer radius ro is placed...

The spool of mass m, radius of gyration kG, inner radius ri, and outer radius ro is placed on a horizontal conveyer belt. The cable that is wrapped around the spool and attached to the wall is initially taut. Both the spool and the conveyer belt are initially at rest when the conveyer belt starts moving with acceleration ac. If the coefficient of static friction between the conveyer belt and spool is μs, determine

(a) The maximum acceleration of the conveyer belt so that the spool rolls without slipping on the belt

(b) The initial tension in the cable that attaches the spool to the wall

(c) The angular acceleration of the spool

Evaluate your answers for m = 500 kg, kG = 1.3 m, μs = 0.5, ri = 0.8 m, and ro = 1.6 m.

Figure P7.46