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 $($Fig$.$ P$8\mathrm{.}67).$ The wheel spins with an angular speed of $17\mathrm{.}5ra\frac{d}{s}$ and its initial angular momentum is directed up$.$ The wheel's moment of inertia is $0\mathrm{.}150kg*m^2$ and the moment of inertia for the student plus stool is $3\mathrm{.}00kg*m^2.($a$)$ Find the student's final angular speed 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?

a

Figure P$8\mathrm{.}67$