In rewinding an audio or video tape, why does the tape wind up faster at the end than at the beginning?

Estimate the magnitude of the tangential velocity of an object in your home town, due to the rotation of the earth.

A small object is sliding inside a circular frictionless track. At point A another frictionless track switches it to a smaller circle (see the picture). At all times the tracks can only exert forces which are perpendicular to the motion of the little slug.
What happens to the linear velocity of the slug when it switches tracks? What about its angular velocity?

A skater is spinning with his arms outstretched. He has a 2 lb weight in each hand. In an attempt to change his angular velocity he lets go of both weights. Does he succeed in changing his angular velocity? If yes, how does his angular velocity change?