Tennis Racket Theorem
Why Physics Stack Exchange recommends it
Physics Stack Exchange answerers point people to it as a quick visual of why rotation about the intermediate axis is unstable, in questions about objects that flip or change their rotation axis.
Recommended by 3 people across 3 different months, 2011 to 2018.
What it is
A 1m42s classroom-style demonstration by Dan Russell showing the tennis racket theorem, where a freely rotating racket or paddle flips over when spun about its intermediate principal axis. The description ties it to Euler's equations and the stability of rotation about principal axes with distinct moments of inertia.
Cited in 1 Wikipedia article, including Tennis racket theorem.
What people said
Recommends Hans de Vries · 2011-11 · Physics Stack Exchange · on “Why does this object periodically turn itself?”
It's a classical mechanics effect for sure although a really interesting one. Following links on "Dzhanibekov effect" one gets at Marsden and Ratiu's "Introduction to Mechanics and Symmetry" [LINK] Chapter 15 Section 15.9 "Rigid Body Stability" treating this with use of the Casimir functions. From remark 1: A rigid body tossed about its middle axis will undergo an interesting half twist when the opposite saddle point is reached . Here is another and more profound example under weightless conditions. [LINK] This seems to be a home experiment where a guy throws the spinning object upwards. [LINK] And this seems to be a computer simulation. [LINK] There is a related unstable orbit effect which
Recommends Mark Rovetta · 2013-05 · Physics Stack Exchange · on “How do objects change their axis of rotation?”
This looks like an example of the Tennis Racket Theorem [this video] . Some axes of rotation for a rigid body are more stable than others. If the initial rotation axis does not correspond to one of the principal axes, a wobble can grow and cause the rotation axis to move to a principal axis. This is a result of Euler's Equations of Motion and the moments of inertia. The tennis racket theorem is a result in classical mechanics [LINK] describing movement of a rigid body with three distinct angular momenta.
Recommends user3294068 · 2018-04 · Physics Stack Exchange · on “Why certain rotations are unstable? (Euler Equations)”
My physics professor helped us visualize this with a tennis racket. Spinning with the axis along the handle is stable. Spinning in the plane of the racket is stable. John McEnroe flipped his rackets like that a lot. Spinning in the other direction, like how you would swing a racket, is unstable. No matter how carefully you flip the racket, it also spins in the other direction before it comes back to your hand. In case you don't have access to a racket to play with: [this video]