A 80 kg astronaut rotates around his space ship on a string. He has a ri = 8 m radius of rotation, and an angular speed of ωi = 4 rad/s. The astronaut pulls himself closer to his ship. His new radius of rotation is changed to rf = 4 m. Assume that the astronaut can be treated as a point mass; the rotational inertia of a point mass is I = mr2.
(a) Compute the final angular speed of the astronaut.
(b) Is rotational kinetic energy of the astronaut conserved? If not, what happened to the difference in kinetic energy? Explain.