Unformatted text preview: 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 height above the ground.
A. The string constrains the rotational and translational motion of the cylinder. What is the relationship between the angular rotation rate and , the velocity of the center of mass of the cylinder? Remember that upward motion corresponds to positive linear velocity, and counterclockwise rotation corresponds to positive angular velocity. Express in terms of and other given quantities.
C. Suppose that at a certain instant the velocity of the cylinder is . What is its total kinetic energy,
, at that instant? Express in terms of , , , and .
, the cylinder's vertical velocity when it hits the ground. , in terms of , , , , and .
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