A person stands on a platform, initially at rest, that can rotate freely without friction. The moment of inertia

of the person plus the platform is IP $.$ The person holds a spinning bicycle wheel with its axis horizontal.

The wheel has moment of inertia IW and angular velocity wW $.$ What will be the angular velocity wP of the

platform if the person moves the axis of the wheel so that it points $($a$)$ vertically upward, $($b$)$ at a $60$ angle

to the vertical, $($c$)$ vertically downward? $($d$)$ What will wP be if the person reaches up and stops the wheel

in part $($a$)?$