Conservation of Angular Momentum and Energy in a Rotating Space Station

[Jenna]

Homework Statement

A space station (moment of inertia 5,000,000 kg•m2) is rotating with angular speed 0.30 rad/s when the 10 inhabitants are in the outer ring (radius 100 m). One half of the inhabitants move to the inner ring (radius 50 m). The average mass of each inhabitant is 70 kg.

a. What is the new angular speed of the space station?

b. How much energy was lost or gained? Where did it go or come from?

c. The rotation of the space station creates the sensation of gravity. Determine the apparent weight of the inhabitants on the inner and outer ring at the faster angular speed.

Homework Equations

Inet=ma
krotational= 1/2I(w)^2

The Attempt at a Solution

For the first part of the problem I attempted to find initial angular speed but I wasn't sure what equation to use, could i use a modified kinematics equation?
For the second part I could use krotational to find the initial energy, but how do I find the final energy? Do i use transitional energy? (But will the astronauts be a discreet mass?)

 

[haruspex]

I attempted to find initial angular speed

You are given the initial angular speed.
What conservation law should you add to your list of relevant equations?