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Conservation of Angular Momentum: Ice skaters and Dumbbells

Author: Jerry Silver

The Idea

How do ice skaters get spinning so rapidly? Where do they suddenly get the energy? Are they violating conservation of energy? This project explores how this works. The term "dumbbells" should in no way be construed to refer to the skaters or the experimenters (or the writer of this book for that matter). They refer to actual dumbbells.

What You Need

  • (low-friction) rotating stool
  • 2 masses, such as a pair of dumbbells (5 kg or greater)
  • 1 person
  • bicycle tire mounted on an axle

Method

  1. Sit on the stool while holding the two masses.
  2. While sitting and balancing on the stool, rotate by pushing off with your feet or by being pushed by someone else.
  3. Lift both feet from the floor.
  4. Start with both masses extended out at arm's length. Then, bring them in close to your body, as shown in Figure 58-1.

Expected Results

Extending your arms slows you down; bringing them closer to your body lets you speed up. The rotational speed (or angular velocity) is greater when the masses are closest to the center of rotation. This works best if the stool rotates very freely with a minimum of friction. The stool can be picked up at a yard sale or purchased commercially. There is also usually less friction for a lower-mass person.

Moment of inertia. Ice skaters and dumbbells.

Why It Works

This project is an illustration of the principle of conservation of angular momentum. Angular momentum for a rotating mass increases either if the object rotates faster or if there is more mass at a greater distance from the center of rotation. If the mass is moved further from the center of rotation, the angular velocity must increase to keep the angular momentum constant.

Other Things to Try

Spinning a bucket on a rope

  1. Sit on the stool with both feet off the floor.
  2. Swing the bucket in a circular path parallel to the floor.
  3. Observe the effect of swinging faster and slower.
  4. Observe the effect of using longer or shorter lengths of rope.

The main thing you notice is you rotate in the opposite direction that the bucket is swung. The faster the bucket rotates in a clockwise direction, the faster you rotate in the counterclockwise direction. A longer section of rope turns you faster than a shorter section.

The Point

A spinning object, such as a skater, must conserve angular momentum. A movement of mass closer to the center of rotation is compensated by an increase in how fast the skater rotates.

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