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Physics: Rotational motion of a mass on a string about a rod. Final speed of the mass.

Mass m is attached to a post with radius R by a string. Initially, the mass is a distance r from the center of the post and is moving tangentially with a speed Vo. In case (a) the string passes through a hole in the center of the post at the top. The string is gradually shortened by drawing it through the hole. Case (b) the spring wraps around the outside of the post. Note that in both cases the mass m moves in a circular motion around the rod.

What quantities are conserved in each case? Find the final speed V of the mass when it hits the post for each case?

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In case (a) the force acting on the mass is all radial. Therefore there's no torque associated with it and angular momentum will remain conserved while the kinetic energy ...

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The solution works out the problem with clear explanations for the answers.