# Unwinding Cylinder

Please do not place your response in a .pdf format, but Word documents are okay. Thanks!

A cylinder with moment of inertia I about its center of mass, mass m, and radius r has a string wrapped around it which is tied to the ceiling. The cylinder's vertical position as a function of time is y(t).

At time t=0 the cylinder is released from rest at a height h above the ground.

(A) In similar problems involving rotating bodies, you will often also need the relationship between angular acceleration, alpha, and linear acceleration, a. Find alpha in terms of a and r.

(B) Find the limiting value of v_f, the final vertical velocity of the cylinder in the following limiting cases:

v_f(I=0)--moment of inertia is zero

v_f(I=infinity)--the limit as the moment of inertia approaches infinity.

In both cases assume that the cylinder's mass remains finite.

Separate your responses with commas. If the limit is infinity, write "infinity".

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#### Solution Preview

A) Let W1,W2 be the angular velocities and V1 and V2 be the linear velocities, then V2 = r*W2, V1 = r*W1

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#### Solution Summary

The solution is given step-by-step.