Laboratory for 3/16/99

ANGULAR MOMENTUM

  1. One person from your group is seated stationary on the rotation platform. This person is handed a bicycle wheel spinning in a horizontal plane. Note the direction of the angular momentum (L) of the wheel. The person now rotates the wheel axis through 180 degrees. Using diagrams indicate what happens and explain the results using conservation of angular momentum.

  2. A member of the group stands on the platform with arms hanging vertically at their side. Give the subject a small angular velocity ( < 1 rps ) and measure this value by finding the time required for 2 rotations. The subject then raises the arms to a horizontal position and the new angular velocity is measured. Do not touch the subject during the procedure.

    Repeat the procedure with 1 kg masses (use 2 kg masses if you can) held in the hands. Measure the distance from the center of rotation to the masses in both the horizontal (ru) and the vertical (rd) positions. Denote the moment of inertia of the person with arms at the side as Id and the moment of inertia with arms held horizontally as Iu.

    The corresponding moments of inertia with  the masses will be (Id + 2m rd2) and (I u + 2m r u2) repectively, where m is the value of the masses . Using both sets of data and conservation of angular momentum, determine the moment of inertia of the subject with hands hanging vertically at their side (Id).

    Find the subject's mass and estimate their moment of inertia assuming they are a uniform cylinder. Make a reasonable estimate for the "radius" of the subject. Compare your estimate to the experimental value found above.

  3. Each member of the group sits on the platform and is handed the bicycle wheel spinning in the vertical plane. Give the subject a small angular velocity. Repeat several times reversing the direction of spin of the wheel and platform. Repeat with the wheel spinning in a horizontal plane. The subject should note the forces and resultant torque necessary to maintain the wheel's orientation. Using top and side view diagrams, show the direction of L, the change in L, and the applied torque t in each case.

  4. A cat with its back to the ground can rotate itself 180 degrees while falling in order to land on its feet. It does this with no initial or net angular momentum ! Can you explain this? First, use the platform and the bicycle wheel to convince yourself that rotations can be achieved without a net angular momentum.

    Seat yourself on the platform and devise a method to achieve a net rotation using your arms and legs. Do not use the friction inherent in the platform by using quick, jerking motions! You may wish to put weights in your hands to increase the effectiveness of arm motions. (A cat has great flexibility that allows for very effective movements.) Describe your method.