Angular Momentum Demos

Equipment:

low-friction turntable
iron bar
weighted bicycle wheel
2 (2-kg) weights
student volunteers

(These are kept in 178 Snell, except for the students)

Demo 1: zero total angular momentum

Get a student to stand on the turntable and hold the bar horizontally over his/her head. Start with everything at rest and the student facing forward. Now ask him/her to rotate the bar in one direction, and then stop. The student's body will rotate in the direction opposite to the bar, and will stop when the bar stops. The rotate the bar back to the original position, and the student should again be facing forward.

There are several points to this simple demo:

At all times L(student)+L(bar)=0, so if the bar turns one way, the student must turn the other.
The relative angles traversed by the student and the bar are inversely proportional to their relative rotational inertia: Delta-theta*I(student)=-Delta-theta*I(bar)
If the net angular displacement of the bar is zero (bringing it around then back) then the angular displacement of the student must also be zero. If, however, the bar returns to its original position by making a full rotation in one direction, the student will generally not be back at his/her original position.

Demo 2: direction of angular momentum

Get another student volunteer to stand on the turntable at rest facing forward. Get the wheel spinning and hand it to the student with the axis vertical and the handle pointing downward. The student should be able to hold it up carefully without rotating on the platform. Then ask the student to invert the wheel so that the handle points upward. The student will start spinning. Now ask him/her to return it to its original position. He/she should come to rest, more of less (different amount of friction in the wheel and the turntable and create a little imbalance after a while).

If we call the initial angular momentum of the wheel Li, then when it is inverted its angular momentum changes to -Li. To maintain conservation of momentum, the student must then acquire an angular momentum of +2*Li.

Demo 3: conservation of angular momentum with changing rotational inertia

This is the classic three-dumbbell demo. Ask for a student volunteer with very strong arms. Good balance and immunity to motion sickness are also good qualities to seek out. Have him/her stand on the turntable holding a 2-kg weight in each arm with his/her arms extended. Get some other students to get him/her spinning, and then ask him/her to pull the weights inward to his/her chest. Of course, the student spins much faster when the weights are pulled inward. If they are extended to arm's length again, you can see him/her slow to his/her original speed. Be careful of dropped weights and dizzy students.

Several points come from this demo:

Since L=I*omega, if you decrease I, you have to increase omega to keep L constant
If you work out the kinetic energy of the system with the arms in and the arms out, you will find that there is more kinetic energy when the arms are in. Ask the students where the energy comes from. The student volunteer who had to pull those weight into his/her chest should have a very good guess.
You can point out other applications of this trick. For example, high divers doing flips tuck their bodies to decrease I and increase omega, and extend their bodies to slow the rotation.