Switch....?

Question

A streetcar is freely coasting (no friction) around a large circular track. It is then switched to a small circular track. When coasting on the smaller circle its speed is:

a) greater
b) less
c) unchanged

Answer 1

Less. On the spiral section of track that provides the transition from larger to smaller radius, the car's velocity has both tangential and radial components. The car must do work to provide the moving centripetal force needed to reduce its radius. Basically the car can be thought of as going up a hill against centrifugal force.
This contrasts with the case of a rotating ball on a string. Someone who reduces the radius of rotation by pulling the string in does work on the ball equal to (the integral of) centripetal force * radius change. On the track, the ball provides the work to accomplish the radius reduction, and thus loses that amount of kinetic energy and corresponding velocity.

Answer 2

Sneaky question. I'll place bets on c. Some people might get it wrong because while the angular velocity will increase, the speed will not change.