A \'\'reference ring\'\' of moment of inertia Ic about the axis shown rests on a

Question

A ''reference ring'' of moment of inertia Ic about the axis shown rests on a solid disk torsion pendulum with a moment of inertia I0 as shown. a) What is the period T0 for the motion with the disk alone? Assume that the torsion constant of the wire is k. (Hint: T = ) b) What is the period T1 for motion with the combined system (ie. when the reference ring is placed on top of the disk and is rotating with it? Assume that the torsion constant of the wire is k. (Refer to last hint) c) Use the expressions from a) and b) to derive and expression for I0 in terms of T0, T1, and Ic. (hint: you will find it most convenient to solve if you take the ratio of the eqations in a) and b))

Explanation / Answer

a) T0=2(pi)[(I0/k)^1/2]

b) T1=2(pi)[(I0+Ic)/k)^1/2]

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