The Bizarre Behavior of Rotating Bodies, Explained

  • 🎬 Video
  • ℹ️ Description
Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation.

References:

The Twisting Tennis Racket

Janibekov’s effect and the laws of mechanics

Tumbling Asteroids

The Exact Computation of the Free Rigid Body Motion and Its Use in Splitting Methods
SIAM J. Sci. Comput., 30(4), 2084–2112
E. Celledoni, F. Fassò, N. Säfström, and A. Zanna

Animations by Iván Tello and Isaac Frame

Special thanks to people who discussed this video with me:
Astronaut Don Pettit
Henry Reich of MinutePhysics
Grant Sanderson of 3blue1brown
Vert Dider (Russian YouTube channel)

Below is a further discussion by Henry Reich that I think helps summarize why axes 1 and 3 are generally stable while axis 2 is not:

In general, you might imagine that because the object can rotate in a bunch of different directions, the components of energy and momentum could be free to change while keeping the total momentum constant.

However, in the case of axis 1, the kinetic energy is the highest possible for a given angular momentum, and in the case of axis 3, the kinetic energy is the lowest possible for a given angular momentum (which can be easily shown from conservation of energy and momentum equations, and is also fairly intuitive from the fact that kinetic energy is proportional to velocity squared, while momentum is proportional to velocity - so in the case of axis 1, the smaller masses will have to be spinning faster for a given momentum, and will thus have more energy, and vice versa for axis 3 where all the masses are spinning: the energy will be lowest). In fact, this is a strict inequality - if the energy is highest possible, there are no other possible combinations of momenta other than L2=L3=0, and vice versa for if the energy is the lowest possible.

Because of this, in the case of axis 1 the energy is so high that there simply aren't any other possible combinations of angular momentum components L1, L2 and L3 - the object would have to lose energy in order to spin differently. And in the case of axis 3, the energy is so low that there likewise is no way for the object to be rotating other than purely around axis 3 - it would have to gain energy. However, there's no such constraint for axis 2, since the energy is somewhere in between the min and max possible. This, together with the centrifugal effects, means that the components of momentum DO change.

💬 Comments on the video
Author

Oh! so thats why my liquid filled bullets keep tumbling!

Author — Cody'sLab

Author

I’m glad the earth isn’t going to flip. If it was, this would be the year for it.

Author — Jeff Oliver

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Oh..., that’s why the bread always lands butter-side down.

Author — Bob in Arizona

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So if all living beings go to the North Pole or South Pole we could flip the Earth!!

Author — João Aurilio

Author

Misread this title as 'The Bizarre Behavior of Rotting Bodies, Explained', here I thought I'd have an explanation as to why cadavers misbehave.

Author — Darth Nox

Author

Video: contains the phrase "prove Feynman wrong"


Also video: doesn't use this phrase as clickbait.


I salute you.

Author — Andrew Chapman

Author

This is why a backflip on the long axis on a skateboard is called an impossible. So a foot has to stop it from flipping.

Author — MuerteFamily

Author

Video: contains the phrase "prove Feynman wrong"


Also video: doesn't use this phrase as clickbait.


I salute you.

Author — Ana Karpova

Author

I wish this guy was my science teacher back in Elementary School, Jr High School, High school, etc..

Author — RadicalRick

Author

They aren't conspiracy theorists, they're conspiracy wingnuts.

Author — Brian Smith

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*Russian Cosmonaut spins a wingnut in space:* _"TELL NO ONE OF THIS!"_

Author — Daniel Renard

Author

I ain’t giving a guy this smart my password, sorry.

Author — 1963 Stratocaster

Author

"Is there an intuitive way of understanding the theorem"
"No"
"We're going to prove you wrong"
> Concludes the intro after 6 minutes of talking.

Author — U1timate1nferno

Author

Once again stack exchange proves to be invaluable towards answering humanities questions: from a compiler error to literally needing the smartest mathematician alive to answer and complicated problem thought impossible to explain.

Author — Scott Maday

Author

This explaination is beautiful when you're actually learning this stuff in school... keeps me wanting to know more. Thanks Veritasium!!!

Author — ılılıᴅᴇᴄɪʙᴇʟılılı

Author

Veritasium: There you have it, an intuitive explanation for the intermediate axis theorem.


Me: Rewatches again at .50x playback speed.

Author — BC

Author

"What are you looking at is the dzhanibekov effect"
Uncultured me: The what

Author — Lap Lace

Author

I'm no longer flipping coins I'm only flipping tennis rackets.. who wants to make a bet??

Author — Corey BROCO

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"The goal of this videdo is to prove Feynman wrong."
**gets popcorn**

Author — jpdemer5

Author

1:18
"And as the wing nut spin off the bolt, he noticed something strange: The wing nut maintained its orientation for a short time, and then it flipped, 180 degrees. And as he kept watching it flipped back a few seconds later, and it continued flipping back and forth at regular intervals."

"This made him focus on the wing nut, and forget about the space station, accidentally killing everyone."

Author — 1salad