# Space Station - Conservation of Angular Momentum

1. Nov 16, 2005

### moo5003

Question:

A space station shaped like a giant wheel has a radius 109m and a moment of inertia of 5.07x10^8 kgm^2. A crew of 180 is living on the rim, and the station is rotating so that the crew experiences an apparent acceleration of .8g. When 140 people move to the center of the station for a union meeting, the angular speed changes. What apparent acceleration is experienced by the managers remaining at the rim? Assume an average mass of 64.0 kg for all the inhabitants.

What I have done thus far:
I = 5.07x10^8
N = 180
N= 40
m = 64.0
A = .8

L = L
L = (I + NmR^2)w
L = (I + NmR^2)w

w' = [(I + NmR^2)w] / (I + NmR^2)

Problem: How do I solve for radial acceleration, when I do not even have the radial speed or the initial speed.

W = Initial + AT ---- Are they asking for radial acceleration or the force felt pushing the inhabitants down on the rim.
Any help is appreciated.

Last edited: Nov 16, 2005
2. Nov 16, 2005

### moo5003

Alright I solved it

Basically I did the following:

Acceleration is the centrifugal force with is equal in magnitude to the centripital force.

Ar = V^2 / 2
V = Root (Ar*R)
w = Root (Ar*R) / R

Substuting that for w and w I arrived at the equation

Ar = [([(I + NmR^2) * Root (Ar*R) / R] / (I + NmR^2)) R ] ^2 / R
Ar = 1.15g Can anyone double check for me.

3. Nov 16, 2005

### Fermat

Check. I got 1.148g