Set the single wheel spinning by running it against the large wheel on the motor. Now, holding the axis of the wheel horizontal, sit on the stool, placing both feet on the red foot rest. Now twist the axis of the wheel about the horizontal line perpendicular to the axis. That is, twist one end up and the other end down. Depending on the direction in which you do this, you and the stool rotate either to the left or to the right.
With the double wheel, if you set both wheels spinning in the same direction, you can show how much more difficult it is to rotate the axis of the wheel than it is to rotate that of the single wheel. You can do something a bit more interesting, though, by setting the two wheels spinning in opposite directions at equal speeds. In this case, the angular momenta of the two wheels are equal and opposite, so that they sum to zero, and changing the direction of the axis about which they rotate results in no change in angular momentum. It is thus easy to do, and when you sit on the stool and twist the double wheels when they are spinning this way, you and the stool do not rotate.
Just as linear momentum is conserved for objects that undergo processes involving linear motion, so is angular momentum conserved for objects that are rotating. Whereas the linear momentum of an object equals mv, where m is the mass of the object, and v is its velocity, the angular momentum of an object equals Iω, where I is the object’s moment of inertia, and ω is its angular velocity. Demonstration 28.45 -- Rotatable stool, dumbbells, illustrates the change in magnitude of ω that must occur if I changes, in order to satisfy this conservation law. This demonstration illustrates what happens if you try to change the direction of the angular momentum vector of a rotating object. Demonstration 28.63 -- Rotating wheel in suitcase, also shows this.
The angular momentum of a rotating object L, as noted above, equals Iω. It points along the axis about which the object rotates, and its sense is given by the right-hand rule. If you curl the fingers of your right hand in the direction in which the object is rotating, then your right thumb points in the direction of the angular momentum vector L.
The large wheel on the motor spins clockwise as you face it, so when you hold the bicycle wheel against it, the top of the bicycle wheel spins away from you. Its angular momentum vector thus points to your left. When you sit on the stool and tilt the wheel, if you tilt the left end of it upward, the change in angular momentum, dL, points upward, which means that you must exert a torque to your left (counterclockwise for an observer looking down at the top of your head). Since you are on a stool that is free to rotate, you cannot provide this torque, so you and the stool turn to your right (clockwise for an observer looking down from above). Another way to put is is that if you point the left end of the bicycle axle upward, since dL, points upward, you and the stool must change your angular momentum in such a way as to keep the angular momentum constant. For you and the stool, then, dL, must point downward; you and the stool must acquire angular momentum in the downward direction, so you and the stool turn to your right, as described above.
If, you tilt the right end of the bicycle wheel axle upward, the change in angular momentum, dL, now points downward. The change in angular momentum for you and the stool must now point upward, and you and the stool turn to your left (counterclockwise for an observer looking down from above).
It is important that when you do this demonstration, you make sure to have both feet clearly on the red foot rest of the stool before you tilt the wheel. This way, you avoid giving the students the impression that you may have caused the stool to rotate by pushing on the floor with your foot.
Using the double wheel, with both wheels spinning in the same direction at similar speed to that with which you set the single wheel spinning, increases the rate at which you and the stool rotate for a given tilt of the axle of the wheels, and also the effort that it takes for you to do this. If you set the two wheels spinning in opposite directions at equal speed, however, their total angular momentum is zero, and it requires no external torque to change the angular momentum of the system. (Tilting the axle of the wheel requires only the torque that it would take if the wheels were not spinning.) You can accomplish this by setting one wheel spinning, then either turning the double wheel around as you face the motor, or turning your back to the motor and backing the second wheel against the drive wheel. Before you get back on the stool, try tilting the axle back and forth. If you feel resistance, give one wheel or the other some more time on the drive wheel. When you feel no resistance as you tilt the axle, you probably have made the speeds of the two wheels close to equal. Once you have done this, if you now sit on the stool, you can tilt the wheel in either direction, and you and the stool stay as you are; you do not rotate.
References:
1) Resnick, Robert and Halliday, David. Physics, Part One, Third Edition (New York: John Wiley and Sons, 1977), pp. 262-263.