Linear speed of car coasting on two tracks

This is another one of those concept problems where if I think about it one way, it makes sense, but if I think about it another way I don’t reach the same conclusion…again, any clarifications in explaining this would be much appreciated.

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 linear speed is…

greater

less

unchanged

2. Relevant equations: kinetic energy = 1/2mv^2

3. Attempt at solution

If I take the system to be the two tracks, earth and the car, then I can consider this as a closed system, where energy is conserved. There is no change in potential energy in the system, and we’ll assume that there is no friction/heat loss. Since in a closed system, no energy enters or leaves the system, and the mass of the car does not change, then we can conclude that the kinetic energy of the car must stay the same, and that the velocity must then be the same.

BUT…what if I try to look at this from a angular momentum approach? It is a closed system and there are no external torques. So then couldn’t you liken this to a revolving ice skater problem? When the ice skater brings his/her arms in, the linear/rotational speed increases. So likewise, when the coasting car transitions to the smaller track, why doesn’t it speed up like the ice skater but just stays at the same speed instead?

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