Princeton University Physics 205

The Tennis Racket Theorem

This, as every tennis player knows, is a consequence of Euler's equation as it applies to the torque-free asymmetric top.

We will explore the theory behind this in class, but as a prelude I encourage you to try it yourself so that you can see what I am talking about.

If you don't have a tennis racket handy, you can perform the same observations using a wooden board, or, say, your physics book. If you use a book, be careful to hold it closed using rubber bands or string. Also, be sure to choose a book (or other object) where all three sides have a different length. If you use something with two equal sides (a CD case for example), you won't see the effect, since it depends on all three moments of inertia being different. (And you may have thought that your CD collection couldn't be considered degenerate!)

Now do the following:

• Toss the book so that it spins about an axis perpendicular to the plane defined by its pages (the "page plane"). You should be able to achieve a fairly smooth spin without too much trouble.

• Next try spinning the book about an axis that lies in the page plane and runs along the long direction. Once again, with modest effort, you should be able to achieve a reasonably smooth spin.

• Finally, try spinning the book about an axis that lies in the page plane, but this time runs along the short direction. Unless you are extremely talented, or extremely lucky, you won't be able to achieve a rapid spin without the book also tumbling or flipping as it goes.

Be sure to dazzle your friends with this, but go a little easy when it comes to regaling them with the wonders of inertia tensors, eigenvectors, and so forth. A little bit of this goes a long way. (If they are in one of overpopulated majors, just tell them it's magic. They won't question you.)