An experimental space station consists of a large rigid rod with length L = 100 m and mass M = 10,000 kg, which rotates about an axis perpendicular to its length and through its center. Two spherical compartments, each containing quarters, laboratory equipment, and science personnel, are attached to the ends of the rod. Each compartment has a total mass of 50,000 kg. The space station rotates such that the compartments experience a centripetal acceleration of 1g (9.80 m/s2). An experiment is performed to test the effect of increased acceleration on physiological processes. During the experiment, each compartment is pulled 25.0 m toward the center of the rod.
a. Calculate the total moment of inertia of the space station (rod plus spherical compartments) before the experiment begins.
b. Calculate the angular momentum of the space station before the experiment begins.
c. Determine the centripetal acceleration experienced by the science personnel during the experiment.
d. Find the work done on the compartments as they are pulled toward the center of the rod.