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A solid sphere of mass, M, and radius, R, is rigidly attached to a strong thin...

A solid sphere of mass, M, and radius, R, is rigidly attached to a strong thin rod of radius r that passes through the sphere at a distance of R/2. A string wrapped around the rod pulls with tension T. The rod's moment of inertia is negligible.

(a) Find an expression for the sphere's angular acceleration.

(b) If the sphere has a mass of 5.5 kg and a radius of 25 cm, how much tension must be applied to the string in order get the system rotating at 6 rev/s in 2 seconds if it started from rest? The radius of the rod is 0.25 cm.

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