A space station shaped like a giant wheel has a radius of 123 m and a moment of

Question

A space station shaped like a giant wheel has a radius of 123 m and a moment of inertia of 5.20 x 10 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 an-by mon than 10% Double cteck your calculations. Need Help? 1 9.P001 MacBook Air

Explanation / Answer

r = 123m , Isi = 5.2*10^8 kg.m^2, N = 150 , a = 1g, n = 150-100=50, m = 65 kg

from conservation of angular momentum Li = Lf
Iiwi =If*wf
ai =g = rwi^2
wi = (g/r)^0.5
wf = (a/r)^0.5
Ii = Isi+Ipi
Ipi = Nmr^2
If = Isf + Ipf
Ipf = nmr^2
((5.2*10^8)+(150*65*123^2))(9.8/123)^0.5 = ((5.2*10^8)+(50*65*123^2))(a/123)^0.5
a = 13.48 m/s^2

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