Suppose a physics instructor seated himself at rest on a low-friction "piano stool" and held a spinning bike wheel with its angular velocity vector initially horizontal. Suppose the instructor then turned the bike wheel so that its angular velocity vector pointed vertically downward. When this turn was completed, the instructor would be spinning rapidly on the stool. What would be the final, total angular momentum of the system of instructor plus bike wheel, projected along the vertical axis, the only axis along which the system can spin?