A student holds a spinning bicycle wheel while sitting motionless on a stool that is free to rotate about a vertical axis through its center (see the figure below). The wheel spins with an angular speed of 17.6 rad/s and its initial angular momentum is directed up. The wheel's moment of inertia is 0.170 kg · m2 and the moment of inertia for the student plus stool is 2.90 kg · m2. (a) Find the student's final angular speed (in rad/s) after he turns the wheel over so that it spins at the same speed but with its angular momentum directed down.

(b) Will the student's final angular momentum be directed up or down?