A cylindrical space station is a hollow cylinder of mass \(M\), radius \(R\), and length \(D\), and endcaps of negligible mass. It spins about its symmetry axis ( \(z\) axis) with angular velocity \(\omega_{0}\).

(a) Find its inertia matrix about its center. A meteor of mass \(m\) and velocity \(v_{0}\), moving in the \(x\) direction, strikes the station very near one of the endcaps, and bounces directly back with velocity \(-v_{0} / 2\). After the collision, find the station's (b) CM velocity (c) angular momentum, both magnitude and direction. (d) Show that subsequently the symmetry axis of the station rotates about the angular momentum vector, so the station wobbles as seen by an outside inertial observer. Find the period of this rotation.