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A cone of height h and base radius R is free to rotate about a fixed vertical axis. It has a thin groove cut in the surface. The cone is set rotating freely with angular speed ω0, and a small block of mass m is released in the top of the frictionless groove and allowed to slide under gravity. Assume that the block stays in the groove. Take the moment of inertia of the cone about the vertical axis to be I0.
a. What is the angular velocity of the cone when the block reaches the bottom?
b. Find the speed of the block in inertial space when it reaches the bottom.

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