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 I_P. The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia omega_W and angular velocity I_W. Take the direction counterclockwise when viewed from above.
Part A: What will be the angular velocity of the platform if the person moves the axis of the wheel so that it points vertically upward?
Express your answer in terms of the variables IW,IP, and ωW.
Part B: What will be the angular velocity of the platform if the person moves the axis of the wheel so that it points at a 60 angle to the vertical?
Express your answer in terms of the variables IW,IP, and ωW.