# Conserved quantities in an angular system

Given the following question:

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 include which of the following?

I) Angular Momentum

II) Linear Momentum

III) Kinetic Energy.

My guess was one and two -- there's no net torque on the system, and as I looked at it, no net force either, as there's not an external actor. Apparently, linear momentum isn't conserved according to the answer set I have. Why is that, in this case?

## 3 Answers

The author of the question may be expecting you to recognize or assume that the axle of the platform is supported by the floor (probably by way of some kind of superstructure), in which case linear momentum would not be conserved for a system defined as the student and the platform because of the reaction between the platform and the floor.

It is, in my opinion, a less than optimal question but not actually atrocious.

• Ah! An open system with undefined boundaries. I rate the question as completely atrocious. May 7, 2015 at 4:19

Your answer set is wrong. Linear momentum is always conserved in closed systems, so your initial guess was correct. Good job! Apparently you know more about physics than the people who write the text books. Also, you should read the policies on posting homework related questions on this site.

Because both the angular momentum and linear momentum are vectors, the direction must be considered. As in this question, the direction of the linear momentum is constantly changing as the circular platform is rotating, and the direction of the angular momentum is always the same (whether out of page or into the page). That's why the linear momentum changes but the angular momentum not.