A uniform thin rod of mass $m$ and length $L$ rests on a flat, frictionless horizontal table. Initially, the rod's center of mass is at rest, and the rod is spinning with angular velocity $\omega_0$ about its center of mass. A small puck, also of mass $m$, is initially at rest on the table. The rod spins until one of its ends strikes the puck, and the puck sticks to the end of the rod. What is the angular velocity of the rod and puck system after the collision? (Answer in terms of $\omega_0$)