A uniform rod of mass 100 g and length 50.0 cm rotates in a horizontal plane about a fixed, vertical, frictionless pin through its center. Two small beads, each of mass 30.0 g, are mounted on the rod so that they are able to slide without friction along its length. Initially the beads are held by catches at positions 10.0 cm on each side of center, at which time the system rotates at an angular speed of 20.0 rad/s. Suddenly the catches are released and the small beads slide outward along the rod.
(a) Find the angular speed of the system at the instant the beads reach the ends of the rod.
(b) What if the beads fly off the ends? What is the angular speed of the rod after this occurs?