A space statA space station shaped like a giant wheel has a radius 99 m and a mo

Question

A space statA space station shaped like a giant wheel has a radius 99 m and a moment of inertia of 5.05 108 kg·m2. A crew of 150 are living on the rim, and the station's rotation causes the crew to experience an apparent free-fall acceleration of 1 g (Fig. P11.27). When 100 people move to the center of the station for a union meeting, the angular speed changes. What apparent free-fall acceleration is experienced by the managers remaining at the rim? Assume that the average mass for each inhabitant is 65.0 kg.
__________m/s2

Explanation / Answer

Is = 5.05*10^8 kg.m^2, mp = 65kg, r =99 m , a1 = 1g

a1 =rw^2

9.8 = 99*w1^2

w1 = 0.3146 rad/s

Initial moment of inertia I1 = Is +(150*mp*r^2)

Final moment of inertia I2 = Is+ (50*mp*r^2)

From conservation of angular momentum

I1w1 = I2w2

(5.05*10^8 +150*65*99*99)(0.3146) = (5.05*10^8 +50*65*99*99)w2

w2 = 0.352 rad/s

a2 = rw2^2/g = (99*0.352*0.352)/9.8

a2 = 1.252g

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