- A solid disk is mounted on a frictionless bearing, so that
it can rotate freely around its center.
It is initially rotating with angular speed
**w**. Alice takes a second circular object -- with the same mass and radius as the disk -- and holds it motionless. She then drops it onto the disk, so that it lands perfectly centered. After a bit of rubbing, the two objects end up rotating with a common speed of**1/3 w**.What type of object did Alice drop onto the disk?

- Jogger Joe (of mass
**60 kg**) stands on his new Circular Treadmill (TM). It is simply a disk of aluminum,**5 meters in diameter**and**10 cm thick**, mounted on a frictionless bearing. Joe steps onto the disk carefully, so that he and the disk are at rest. Joe then begins to jog at the outer edge of the disk. After a while, he reaches a steady pace, so that the disk rotates**once every 136 seconds**.- What is the angular velocity of the disk?
- What is the angular momentum of the disk?
- What is Joe's angular momentum around the center of the disk?
- What is Joe's angular velocity?
- How fast is Joe jogging? Compute the linear speed of his feet, relative to the disk.

Answer to the treadmill problem

- The handle of a broken hockey stick,
of length
**L = 1.3 m**and mass**M = 320 grams**lies motionless on the ice. One end is pegged to the ice, but the stick is free to pivot around that point. A hockey puck of mass**M = 160 grams**slides across the ice towards the end of the rod with a speed**v = 10 m/s**.- What is the total kinetic energy of the system as the puck approaches the stick?
- What is the angular momentum of the puck around the
pivot point when it is
**4 m**from the stick? - What is the angular momentum of the puck around the
pivot point when it is
**3 m**from the stick? - What is the angular momentum of the puck around the
pivot point when it is
**2 m**from the stick? - What is the angular momentum of the puck around the
pivot point when it is
**1 m**from the stick? - What is the angular momentum of the puck around the pivot point when it reaches the stick?
- What is the angular velocity of the stick-plus-puck as they pivot?
- What is the rotational kinetic energy of the stick-plus-puck?
- Was kinetic energy conserved in this collision?

The puck hits the end of the rod and sticks to it. The rod and puck start to rotate around the pivot.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.