Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Someone once mentioned to me that it's impossible to throw a tennis racquet (or similarly shaped object) into the air, perpendicularly to the string plane, in such a way that it won't turn.

What is this effect, or was he talking rubbish?

share|improve this question
For the Dzhanibekov effect, the tennis racquet theorem, and the intermediate axis theorem, see e.g. physics.stackexchange.com/q/17504/2451 and links therein. –  Qmechanic Jul 6 '12 at 21:53
add comment

2 Answers

up vote 3 down vote accepted

The "effect" is quite real, but I don't believe there's a name for it. It has to do with rotational stability and the intermediate axis theorem.

I'm sure you've also observed this effect when throwing a spatula, frying pan, or remote control.

In terms of rotational inertia, the "easiest" axis of rotation for the racquet is straight through the handle. The "hardest" axis of rotation would be straight down (perpendicular to the strings).

But when there's rotation along the "intermediate" axis (the one you describe), the other axes (especially the "easiest") become extremely sensitive to random perturbations.

If you could flip or spin the racquet so that it turned exclusively about one of its three principal axes, it would continue to spin about that axis indefinitely. That's why they're called principal axes. But in a real flip there is always some mixture of motions about all three axes. Here is where the intermediate axis theorem enters the picture: while a racquet spinning mostly about either the low-rotational-inertia axis or high-rotational-inertia axis will be relatively unaffected by extraneous motion about the other two axes, a racquet that is spinning mostly about the intermediate-rotational-inertia axis is exquisitely sensitive to any accidental motion about those other two axes. Even a tiny amount of unintended motion about those axes will cause the racquet to wobble significantly.

share|improve this answer
add comment

See this thread on math overflow. (And the nice videos in the question and the answers.)

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.