How Does Crew Movement Affect Acceleration on a Space Station?

[Brocoly]

Homework Statement

A space station shaped like a giant wheel has a radius 95.0 m and a moment of inertia of 5.03✕ 10^8 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.

Homework Equations

ac=rw^2
L=I1w1=I2w2
I=mr^2

The Attempt at a Solution

w1=sqrt(9.81/95)=0.32135
mass of station= I1/r^2 - Mass of people=45984kg
I2=(45984+(50)(65))r^2=4.44*10^8
w2=I1w1/I2=0.36
ac=r(0.36^2)=[12.3]
but this doesn't seem to be the right answer.

 

[dillon13]

You've done it right - just don't round your numbers before your final answer!

 

[NascentOxygen]

I'd read it as saying the mass of the station (unmanned) = 5.03x10^8 / r²

 

[Brocoly]

Oh so the moment of inertia is 5.03e8 when when the mass of the station is combined with the mass of people?

 

[BvU]

No, but $\omega_2$ = 0.3638 gives a sligtly different answer.

Another possibility is that if they start with apparent acceleration 1g in the exercise, they want you to express the answer in terms of g too...

Nascent also has a good point: 5.03e8 for the unmanned station gives 5.91e8 if all 150 are on the rim.

When you (and I ) write "mass of station= I1/r^2 - Mass of people=45984kg" we assume the 5.03e8 includes the 150 people.