Football, skaters and stars

As figure skater Yuko Kawaguti folds in her arms, she spins faster. Photo: deerstop

See that football flying across the field, not wobbling or tumbling but spinning around its axis. Easier to catch than the wobbler, right?

Watch a figure skater doing a pirouette, bringing her outstretched arms to her side and whirling faster, then stretching out her arms and slowing down. Her action would be more dramatic, but not as pretty, if she carried heavy bricks in her hands.

Last month I mentioned a 20-kilometer-diameter collapsed star, called a pulsar, spinning at 10,000 rpm. It used to be a huge star spinning slowly, but when it went supernova and collapsed, it spun faster. Less elegant than the skater, but much more dramatic!

These things are all consequences of a physics law about a concept called angular momentum.

If you have been hit by a ball – or a bat — you probably have a good feel for “momentum.” It is the mass times the velocity. The hurt would be the same if the weight was doubled and the speed halved, or the other way around, since it is the product that counts. Now, I just said “speed” for simplicity, but I should really say “velocity,” which has a value (the speed) and a direction, pointing forward like an arrow. A directional quantity is called a vector.

Angular momentum is simply the momentum — for example, of the skater’s bricks — multiplied by the distance from the axis of her spin, above the point where her skates touch the ice. Angular momentum is also a vector, pointing along the spin axis.

In 1915, Emmy Noether, a brilliant mathematician, proved a very profound theorem using just her brain, her knowledge of mathematics, a pencil and paper. According to Einstein, she was the most significant mathematical genius produced since the higher education of women began. I doubt whether Noether visualized the following thought experiment, but Einstein probably did:

Imagine being in a windowless laboratory floating in space, with no gravity to tell up from down or sideways. No experiment can tell you your orientation; the laws of physics do not depend on direction in space. If that is true, Noether proved that the total angular momentum of the system cannot change. We say it is conserved.

That is why the football keeps pointing in the same direction. It is also why, when our skater brings her arms to her body, reducing their distance, she spins faster.

Just hope she does not let go of those bricks!

This is a version of an article that originally appeared in Positively Naperville.