Conservation of Angular and Linear Momentum

[Jzhang27143]

Homework Statement

A student initially stands on a circular platform that is free to rotate without friction about its center. The student jumps off tangentially, setting the platform spinning. Quantities that are conserved for the student-platform system as the student jumps include which of the following?

I. Linear Momentum
II. Angular Momentum
III. Kinetic Energy

Homework Equations

F = dp/dt, T = dl/dt

The Attempt at a Solution

The answer is only angular momentum. However, I do not understand why angular momentum is conserved but not linear momentum. Since the system consists of the student and the platform, the force of the student on the platform and the reaction force are internal forces. They don't contribute to external force or torque. Am I missing something?

 

[SammyS]

Homework Statement

A student initially stands on a circular platform that is free to rotate without friction about its center. The student jumps off tangentially, setting the platform spinning. Quantities that are conserved for the student-platform system as the student jumps include which of the following?

I. Linear Momentum
II. Angular Momentum
III. Kinetic Energy

Homework Equations

F = dp/dt, T = dl/dt

The Attempt at a Solution

The answer is only angular momentum. However, I do not understand why angular momentum is conserved but not linear momentum. Since the system consists of the student and the platform, the force of the student on the platform and the reaction force are internal forces. They don't contribute to external force or torque. Am I missing something?

If the platform were completely free to move, both would be conserved. But the center of the platform apparently doesn't move.

 

[Doc Al]

Am I missing something?

You are missing the external force from the platform's axle, which is presumably attached to the ground. If it wasn't fixed in place, then linear momentum would be conserved.

 

[haruspex]

The question isn't quite right, and that may lead to your confusion.
Angular momentum is only meaningful in terms of some reference point. In the present case, the question assumes that reference point is the axle of the platform. If you were to take any other reference point it would not be conserved.
Given the answers by Doc Al and SammyS, do you see why the axle is special here?