Question

A space station shaped like a giant wheel has a radius of 109 m and a moment of inertia of 4.96 times 10^8 kg. m^2. A crew of 150 lives on the rim, and the station is rotating so that the crew experiences an apparent acceleration of 1 g. 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. m/s^2

Answer 1

Ii = 4.96*10^8 kg.m^2, r =109 m , ai =1g,

angular acceleration αi = a/r =9.8/r

from coservationtion of momentum

Iiαi = Ifαf

If = Ii - m*150*r^2

(4.96*10^8*9.80/r = (4.96*10^8 - (65*150*109*109))(af/r)

af =12.79 m/s^2