A space station shaped like a giant wheel has a radius 97 m and a moment of inertia of 5.08 108 kgm2. A crew?

Question

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A space station shaped like a giant wheel has a radius 97 m and a moment of inertia of 5.08 108 kgm2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1 g (Fig. P8.54). 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.
m/s2

Answer 1

Angular momentum=moment of inertia* angular velocity
conservation of angular momentum applied to before and after the move.

Answer 2

via I(preliminary) = I(station) + I(persons) =>I(preliminary) = 5.09 x 10^8 + a million/2 x one hundred fifty x sixty 5 x (ninety 5)^2 =>I(preliminary) = 5.fifty 3 x 10^8 kg-m^2 given a = 9.8 m/s^2 =>via a = v^2/r or r?^2 {as v = r?} =>9.8 = ninety 5 x ?^2 =>? = ?0.10 =>? = 0.32 rad/sec subsequently L(preliminary) = I(preliminary) x ?(preliminary) =>L(i) = 5.fifty 3 x 10^8 x 0.32 = a million.seventy 8 x 10^8 ----------------(i) 2d undertaking:- =>I(very final) = 5.09 x 10^8 + a million/2 x 50 x sixty 5 x (ninety 5)^2 = 5.24 x 10^8 kg-m^2 via the regulation of angular momentum conservation:- =>L = I1?1 = I2?2 =>?2 = (a million.seventy 8 x 10^8)/(5.24 x 10^8) =>?(very final) = 0.34 via a = r?^2 =>a = ninety 5 x (0.34)^2 =>a = 10.ninety 8 m/s^2 OR =>a = 10.98g/9.8 = a million.12g