Max % Change in Station Angular Speed Due to People Movement

[franknew]

Homework Statement

A cylindrically shaped space station is rotating about the axis of the cylinder to create artificial gravity. The radius of the cylinder is 82.5 m. The moment of inertia of the station without people is 3.00 x 10^9 kg m^2. Suppose 500 people, with an average mass of 70.0 kg each, live on this station. As they move radially from the outer surface of the cylinder toward the axis, the angular speed of the station changes. What is the maximum possible percentage change in the station’s angular speed due to the radial movement of the people?

Homework Equations

I think it is:
mgh + 1/2mv^2 + 1/2Iw^2 = 1/2mv(f)^2 + 1/2Iw(f)^2

The Attempt at a Solution

I have an example that the teacher did that I think is sort-of the same thing using the above formula. I'm just not sure how to use it with my question.

Any help is much appreciated.
Thanks,
Frank

 

[ideasrule]

You're using a conservation of energy equation. That has a few problems:

(1) Energy is not necessarily conserved; some energy is lost when the astronauts move along the spaceship.
(2) mgh is gravitational potential energy, but this artificial gravity is non-uniform; it doesn't have a constant g.

Instead, use the conservation of angular momentum, which always applies in the absence of outside torque. Of course, the station's moment of inertia changes when people move from the outside to the axis, and you have to take that into consideration.

 

[franknew]

You're using a conservation of energy equation. That has a few problems:

(1) Energy is not necessarily conserved; some energy is lost when the astronauts move along the spaceship.
(2) mgh is gravitational potential energy, but this artificial gravity is non-uniform; it doesn't have a constant g.

Instead, use the conservation of angular momentum, which always applies in the absence of outside torque. Of course, the station's moment of inertia changes when people move from the outside to the axis, and you have to take that into consideration.

So instead of using Ekin=1/2mv^2, I will use Ekin=1/2Iw^2?

I think I need to do the calculation when r=82.5m for when the people are at outer edge of the cynlindrical satellite and then do another when r=0m for when the people are at the axis. I'm just not sure how I can do this with the equation I have.