Unwinding Cylinder (Moment of Inertia; Angular Rotation)

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.

**Please see attachment for complete question including diagram

Unwinding Cylinder
A cylinder with moment of inertia about its center of mass, mass , and radius has a string wrapped around it which is tied to the ceiling .
The cylinder's vertical position as a function of time is .
At time the cylinder is released from rest at a ...

Solution Summary

The expert examines unwinding cylinder for the moment of inertia for angular rotation.

A solid, horizontal cylinder of mass 10.4 kg and radius 1.13 m rotates with an angular speed of 6.81 rad/s about a fixed vertical axis through its center. A 0.251 kg piece of putty is dropped vertically onto the cylinder at a point 0.864 m from the center of rotation, and sticks to the cylinder. Determine the final angular speed

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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

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See attached file for full problem description.

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