A space station shaped like a giant wheel has a radius of 105 m and a moment of

Question

A space station shaped like a giant wheel has a radius of 105 m and a moment of inertia of 4.53 108 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 apparent acceleration is experienced by the managers remaining at the rim? Assume that the average mass of each inhabitant is 65.0 kg.

I have followed along with other problems but I am getting an error within 10% and cannot figure out where I am off. I am getting 13.8294. The last post to this problem was incorrect

Explanation / Answer

Here ,

radius of wheel , r = 105 m

initial angular speed is wi

as a = w^2 * r

9.8 = wi^2 * 105

wi = 0.306 rad/s

Now , let the final angular speed is wf

Using conservation of angular momentum

Ii * wi = If * wf

0.306 * ( 4.53 *10^8 + 150 * 65 * 108^2) = wf * ( 4.53 *10^8 + 50 * 65 * 108^2)

wf = 0.353 rad/s

now , final angular accleraion = wf^2 * r

final angular accleraion = 0.353^2 * 105

final angular accleraion = 13.1 m/s^2

the final angular accleraion is 13.1 m/s^2

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