Physics questions about angular, linear momentum?

Well, this is a slightly irritating problem, because it can come down to a matter of interpretation.

To get rid of the easy one, Kinetic Energy is of course not conserved - one need only remember that KE is a scalar quantity, and a measure of the "energy of motion", and that when two things go from "not moving" to "moving", that there is of course a change in total kinetic energy (as there is no "negative" energy).

Now here's where it gets a bit iffy. If you want to consider the TOTAL momentum of the system, then momentum should be conserved.

However, if you consider linear momentum and angular momentum as separate things... then neither is conserved. Consider that at the start, both the student and the platform are at rest. The student jumps off, causing the platform to rotate. Now, how is linear momentum conserved?

Well, if we look at the student in motion, he has linear momentum going in some direction. The point that he just left (on the platform) is now moving away in the opposite direction, so if linear momentum is conserved then it stands to reason that it accounts for the student's new momentum, right? Well, let's not forget that a point opposite that point on the platform is moving in exactly the opposite direction as our take-off point... so all told the linear momentum of the platform equates to zero. Since the platform doesn't have linear momentum to counter the student's momentum, linear momentum cannot be conserved.

Now consider the angular momentum of the platform. Before, it wasn't spinning. After, it's in the midst of spinning, and thus has angular momentum. What about the student? Well, we just established he has linear momentum, but there's no longer any force causing him to move centripetally, and as such he no longer "rotates" about the center of the platform. In the same way that linear momentum isn't conserved, thus, angular momentum is not.

Only Kinetic is not conserved. Think of it as a sticky collision. Easy if you run the movie backwards. A hits B, sticks and stops. The system is the two together, so total linear and angular momentum are conserved. Of course individual momenta are not conserved.