Questions 1-3 deal with Conservation of Angular momentum.

1. A solid disk is mounted so it can rotate without friction about an axis through its center. Initially it rotates with some angular velocity w. A second object, initially not rotating, is dropped onto the disk. The second object has the same mass and radius as the disk. When the two come to a common rotation, the final angular velocity is 1/3 of the original. What is the shape of the second object?

2. A thin rod of mass 9.0 kg and length 0.80 m is pivoted at one end and can rotate without friction along a horizontal surface. Initially it is rotating clockwise at 1.2 rad/s. A piece of putty of mass 50 grams moves toward the end of the rod as shown with a speed of 60 m/s. The putty collides and sticks to the rod at the location illustrated. What is the final angular velocity?

Now you will need to consider Conservation of Energy and Conservation of Momentum (either linear or angular).

3 . The same rod is hung vertically, and now it is initially at rest. The same piece of putty is shot at the bottom end with some speed, hits the rod and sticks to it, and now the rod plus putty swing up. When the rod and putty momentarily come to rest, the rod makes an angle of 76° with the vertical. What is the speed of the putty?

4. Now we go back to the sheet of ice that is frictionless. On it we place a rod, but now the rod is not pivoted. I shoot a rubber ball that makes an elastic collision with the rod. After the collision, find the velocity of the ball. You can do in symbols or use numbers: Rod L = 4.0 m, mass M = 0.600 kg. Ball m = 0.400 kg, initial speed v0 = 5.00 m/s. Hint: for angular momentum, use an axis that is at the initial COM of the rod. [Interactive Physics Simulation: BallAndStick]

BONUS 5. In a scratch spin in figure skating, a skater begins to rotate with her arms extended straight out at some angular velocity, she then pulls her hands in tight to her body and rotates at a larger magnitude angular velocity. Estimate the ratio of the angular speeds.

This page maintained by Anne G. Young. Last modified 24-Mar-2005 .