|Begin with the wheel rotating so that its angular momentum is upward. The man and the stool are at rest. The stool is on a bearing mount so that it can freely rotate.
||If the wheel is turned over, its angular momentum is now downward. But since there is nothing to exert a significant torque on the system, the angular momentum must have the original value upward. The man and the stool begin to rotate with angular momentum twice that of the wheel.