# A spinning space station exhibits a change in moment of inertia.

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1. Nov 6, 2014

### MacRowan

1. The problem statement, all variables and given/known data

A space station shaped like a giant wheel has a radius 95.0 m and a moment of inertia of 5.03✕ 108 kg · m2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1g. When 100 people move to the center of the station for a union meeting, the angular speed changes. What acceleration is experienced by the managers remaining at the rim? Assume that the average mass of each inhabitant is 65.0 kg.

So,

r = 95.0

I = 5.03*108

and

m
ave = 65.0 kg

Δm = 150*m
ave - 100*mave, or mf - mi

2. Relevant equations

Li = Lf ---> (Iω)i = (Iω)f

ac = rω2, and therefor, w = √(acr)

I = mr2

3. The attempt at a solution

A reminder; I'm looking for the new centripetal acceleration felt by the remaining 50 New Earth colonizers.

I also want to clarify that I chose to determine the total initial moment of inertia by adding the I of the people to that of the provided I for the space station, because I reasoned I couldn't really find the difference without being provided the mass of the space-station, so I'm already unsure of my path here.

There is a change in moment of inertia of the system, so;

Li = Lf

Ii = (I150people) + (5.03*108) = (5.910*108

If = (I50people) + (5.03*108) = (5.350*108

but to find centripetal acceleration I need to relate ac and ω, and then put them into the conservation equation like so;

(5.910*10^8)*(√9.81*95.0) = (5.350*10^8)*(√ac*95.0)

When I isolated acceleration I got a value of 1.859, which my shitty electronic feedback java program says is more than 10% off. At least it's a smaller value, as it should be.

So, obviously I don't have the right answer, but can someone either point out my small error or point out how I have approached the problem entirely wrong?

2. Nov 6, 2014

### ehild

Welcome to PF!

First, ac=w2R, so your last equation is not correct. But you can simplify by R, so it does not really count.
I just wonder, how did you get 1.859 m/s2 for ac, or was it 1.859 g?. You miscalculated something.

Last edited: Nov 6, 2014
3. Nov 6, 2014

### PhysX

You're on the right track but w= sqrt(acr) doesn't seem to be correct... which is affecting your last equation.
Your If seems a little off but should be fine for the purpose of this question.
I just got an answer using your values, only correcting the formula for w, and web assign accepted it as a correct answer.