4. A giant space station in the shape of a wheel is being
evacuated. The space station is rotating about an axis
through its center of mass that is perpendicular to the
wheel. Each wave of evacuees consists of one thousand
4.000 x 10³-kg escape pods (where the pod mass includes
the passengers, originally included in the mass of the
system). Assume the launchers are constructed such that
the pods leave the station with a velocity directed straight
outward from the rotation axis. Model the pods-station
system before the release of the first wave of evacu-
ees as a cylindrical hoop of radius 1.800 km and mass
1.000 x 108 kg rotating at a rate of 2 rad/min. The rota-
tional inertia of a hoop with mass M and radius R is MR².
(a) Explain why the ejection of the pods changes the rota-
tional speed and angular momentum of the station
itself but does not change the angular momentum of
the pods-station system.
(b) Calculate the change in angular speed of the station
after the first wave of evacuees has left the station.
Express your answer in rad/s.
(c) Now, assume the pods had been released from rest rela-
tive to the surface of the rotating station, not launched.
Provide a paragraph-length explanation of the motion of
the pods, and whether or not the angular speed and/or
angular momentum of the station changes in this case.