A space station shaped like a giant wheel has a radius 99 m and a moment of iner

Question

A space station shaped like a giant wheel has a radius 99 m and a moment of inertia of 4.93 ? 108 kg

A space station shaped like a giant wheel has a radius 99 m and a moment of inertia of 4.93 ? 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

Explanation / Answer

total moment of inertia along with 150 people

I=4.93*10^8 +150*65*99^2

=5.89*10^8 kg.m^2

now angular velocity

a=w^2*r

w=0.31 rad/s

Applying conservation of momentum

I1w1=I2w2

I2 when 100 people moves at the centre

4.93*10^8 +50*65*99^2

=5.25*10^8 kg-m^2

So we have

5.89*10^8 *0.31=5.25*10^8*w2

w2=0.35 rad /s

a=w^2*r

=11.97 m/s^2 ans

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