Unwinding Cylinder (Moment of Inertia; Angular Rotation; Velocity of Center of Mass; Positive Linear Velocity)

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.

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