Assignment:
Question 1. 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.