> temp > à-trier > the-intermediate-axis-theorem-veritasium

The Bizarre Behavior of Rotating Bodies, Explained

Veritasium - 2019-09-19

Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation.
Part of this video was sponsored by LastPass, click here to find out more: https://ve42.co/LP

References:
Prof. Terry Tao's Math Overflow Explanation: https://ve42.co/Tao

The Twisting Tennis Racket
Ashbaugh, M.S., Chicone, C.C. & Cushman, R.H. J Dyn Diff Equat (1991) 3: 67. https://doi.org/10.1007/BF01049489

Janibekov’s effect and the laws of mechanics
Petrov, A.G. & Volodin, S.E. Dokl. Phys. (2013) 58: 349. https://doi.org/10.1134/S1028335813080041

Tumbling Asteroids
Prave et al. https://doi.org/10.1016/j.icarus.2004.07.021

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
https://doi.org/10.1137/070704393

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.

Cody'sLab - 2019-09-30

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

Dave95sk - 2021-02-22

I love science community in YouTube <3 I wish we could share all the knowledge each human has directly between brains like a server, it would be awesome and we could do so many cool things. Is this the future of Block Chain? Who knows :) Quite scary though..

Thomas Rogers - 2021-03-10

@Clifford S. I get the same effect with bacon grease.

Thomas Ascher - 2021-03-15

@Steelehead .nn

linkbirds - 2021-03-21

that sounds psychotic

wozal - 2021-03-21

@Randomly yeah it's amazing what other people are thinking sometimes lol

ılılıᴅᴇᴄɪʙᴇʟılılı - 2020-11-15

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

Rita Maru - 2021-02-20

@Malcolm Taylor Good

gorilla·ganja - 2021-03-08

nbmvmvmnmvmcmvmvmvmmmmnnnbnbb;bmk I k m imi ii ll bean 8

who? - 2021-03-11

I would probably agree in a few years

Hans Jakob Rivertz - 2021-03-16

​@Malcolm Taylor Last fall, this was my students school work. :-)

ShonenAce - 2021-03-16

same

Ethan Yu - 2020-12-05

The Earth should flip... let Australians get a chance to feel what it's like to be upright for the first time in their Iives.

Jerome Goodwin - 2021-03-13

The liquid center of the earth does flip at times/ Thus the compasses will change N and S.

Psychentist - 2021-03-16

@Jerome Goodwin Thanks, you beat me to it!

FourTre Northcyda - 2021-03-17

Its currently on its side, thus your moon appears to rotate clockwise in the Northern hemisphere, counter clockwise in the southern.
A energy follows thru an inertial plane.
Scalar physics, magnets aswell

꧁RadicalRick꧂ - 2020-10-03

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

Alfred James - 2020-11-30

I wouldn’t want to learn about physics in elementary school, but other then that I agree with you.

Robin Brown - 2020-12-29

In high school our physics teacher taught us electrical resistance by putting wires in both ends of a hot dog, plugging it into an electrical outlet and cooking it then put it in a bun and eating it.

Alfred James - 2020-12-29

@Robin Brown That’s theteacher I want

Weechie - 2021-01-17

@Bollibompa 👍💯😯🙋😉

Rita Maru - 2021-02-20

He would make everyone in the class a scientist

1963 Stratocaster - 2020-10-02

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

Parth Srivastav - 2020-11-16

Didn't get it

Tohru Bot - 2020-11-22

Great video. You describe the spinning object as being “bumped,” and that triggers the cascade of axis flipping. I assume that bump comes from the air resistance, or maybe from an imperfect spin. What if you eliminate Those? A vacuum has no air; will the wingnut still flip? Do imperfections in the initial spin affect this phenomenon at all?

Weechie - 2021-01-17

@Tohru Bot I think so.. spinning objects seeking their own angular momentum,, seen it happen with toys with gyros.

James Villacorta - 2021-03-01

MOTHER EARTH WILL TURNOVER ??
HOPING NOT IN MY LIFETIME ..HA HA HA HA HA HA

ADAM - 2021-03-11

tabiki hayatta kalınırsa.

Daniel Renard - 2019-09-19

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

Weechie - 2021-01-17

@Joe Yup.. yikes 😯

Daryl Cheshire - 2021-01-26

@Lawrence yonge It’s called Pellucidar

Lawrence yonge - 2021-02-02

@Daryl Cheshire Thank you.

Drew Hurst - 2021-02-05

@fletchkirk Plenty of evidence that You're right. The message to the masses is always "everything is going to be OK"

vaibhav k - 2021-03-01

@Androvsky Actually, more strategically, Russians did not want Americans learn this and get an upper hand in the times of race to the space (and thereby, the war in the space), especially when it seemed so real and so near.

And to be fair, I think they got their reward since, as the video said it, Americans learnt it the hard way by losing a couple of their satellites to it in the fierce times of the space race.

MuerteFamily - 2020-10-10

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.

RobGBarker182 - 2020-10-12

Physics girl on YouTube has a great video with Rodney Mullen talking exactly this. https://www.youtube.com/watch?v=yFRPhi0jhGc

Markus Seppälä - 2020-10-12

That's cool never thought about it that way.

MuerteFamily - 2020-10-12

RobGBarker182 yes that’s how I know this! That was a great video like this one!

Joe D - 2020-11-18

So a hard flip should be called an inevitable flip...

RobGBarker182 - 2020-11-18

@Joe D Haha I like it, although my understanding is a hardflip was a FS Shove with a kickflip, or a frontside flip without the body rotation, I could never land one either way lol

Darth Nox - 2020-10-07

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

Regina Phalange - 2020-10-21

LMAO!

Yuniko Yato - 2020-11-20

all the covid dead coming back?!

Andrew Herman - 2020-11-27

@Roger Felton it's your epididymis that gets tangled up! Ouch

Sho Tor - 2020-11-29

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

nghesi bartender - 2020-12-11

"Janibekov's rotating nut has caused astonishment"

oh ladies~

Beth Heller - 2021-02-12

"If you are relieved that the earth will no longer flip over" implies that it was going to flip unless we found a way to mathematically prove otherwise. I thought that was funny

Devin Nall - 2021-02-14

And the Russians told nobody

Science Is All - 2021-03-14

That’s the way goofy mathematicians think

Science Is All - 2021-03-14

Just like the quantum nuts

João Aurilio - 2020-10-10

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

Ashida - 2020-12-21

Well better than that we make mega dam like three George Dam in China where water hold up in large volume and start to find the equilibrium.

Weechie - 2021-01-17

Water being heavy, the huge hydro-dams, like Three Gordges in China,, are known to affect the earth's balanced spin.

half chair - 2021-01-19

@Larry Dutton deep

Larry Dutton - 2021-01-21

@half chair Not meant to be...more like glib, dude.

ProgrammerPC Theory - 2021-01-22

The earth will reset the change through water movements or movements of the liquids in the deeper layers, so it might be a small impact but not too major to cause a flip

NLTops - 2020-03-07

Someone should tell the Flat Earthers of the Dzhanibekov Effect. They'll freak out and think that sooner or later their precious disc world will flip and they'll all fall off.

꧁RadicalRick꧂ - 2021-02-20

I'm waiting for it to flip back over because I'm hanging on by a thread here!

beryl - 2021-03-01

For those keeping track; this conversation fails every single maxim and submaxim of Grice's Cooperative Principle. My rule of thumb, if the goal really is discourse, is to disengage entirely if more than one maxim is broken, for the sake of my own time/sanity.

NLTops - 2021-03-01

@beryl Frankly, not a bad general strategy. But to be fair, my joke wasn't intended to start any discourse. Flat Earthers are basically the "We have the right to be stupid" movement. And it's true, they have. But whether to be proud of that is a different question.

John Klumpp - 2021-03-05

@DutchObserver Last century a collection of 3.5" discs formed a good backup of one's Hard Disk.

peepoo - 2021-03-06

@Robert Rudd Why do you talk like those annoying people in fairytales that only talk in rhymes

U1timate1nferno - 2020-10-12

"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.

Stefan Schleps - 2020-11-22

My point exactly !

pkgfx. - 2020-10-16

Who else just started flipping their phones??

Thomas Johnston - 2020-10-21

Grabbed a book instead

aforementioned dude - 2020-10-29

Yep I did for like 5 minutes and it always twists.

Daniel Craig - 2020-12-29

maybe we should ao a video about this.

damag3plan - 2021-01-13

That was actually more logical than I thought it would be

M. A. - 2021-03-13

Can galaxies be flipping too? Would that explain the dark energy?

The Pizza Guy - 2021-03-23

I don't know how those two things would be connected at all, but who knows. I'm certainly not a scientist

Andrew Chapman - 2019-09-19

Video: contains the phrase "prove Feynman wrong"


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


I salute you.

fopperer - 2020-10-12

@Andrew Chapman its true

Andrew Chapman - 2020-10-12

@fopperer He's one of the most famous physicists of all time my g.

fopperer - 2020-10-12

@Andrew Chapman dude, you dont get it, do you...

Andrew Chapman - 2020-10-12

@fopperer If there's a pun or something then I've missed it.

Luke - 2020-11-16

@Living Legend idk man his students were pretty clever on average...

Blue Raja - 2021-03-10

8:51 why doesn't this also apply to the other axis of rotation, where the situation is the exact same but the masses are swapped?

Boris Spacek - 2021-02-16

I've noticed this with my phone for years. When I take it out of my pocket, it's the wrong way around, and most times I can just give it a toss and it rights itself, with the screen facing me.

Rainbow bun - 2021-03-17

13:49
Video: “And that’s—“

Add: “that’s life...”

Mind Hacker - 2020-10-09

2:00 ive experienced this pain for 5 years now, and still dont know why my tv remote doesnt flip on a singular axis, guess im about to find out

latiremo - 2019-11-27

when the world flips over, we’ll become fake and australia will become real

MR Sheep - 2020-10-13

That is kinda offensive because I am Australian and you are basically saying that I am non-existent

This Zombie Bites Everything - 2020-10-13

@MR Sheep yeah,he is making a joke about the flat earthers who believe Australia is not real and that we are all actors saying that Australia is real... as an Aussie myself, I find people who believe we ain’t real to be dicks, but I think this guy was just making a joke(clearly the joke could do with some context).

latiremo - 2020-10-13

@MR Sheep clearly you’ve never heard of the “australia is not real” meme. it’s been a running joke; if you can’t take a joke you should stay away from the internet

League Master gg - 2020-10-14

it would be the land up above

John Klumpp - 2021-03-05

"And he said:
I come from a land down under
Where beer does flow and men chunder
Can't you hear, can't you hear the thunder?
You better run, you better take cover, ye-aah"

Xander Blake - 2020-10-13

If continents move, and water moves, doesn't that mean the maximum moment of inertia can change?

Luw Ida - 2020-11-11

My guess would be no, angle of spinning/tilt may change.

Auna - 2021-01-13

that may be why there is north and south pole movements over the course of the history of the world.

Jase Te Ace - 2021-01-22

Yes it does. The point is that it has done so already. We are now in the most stable mode of rotation. Those things would only move if it made Earth even more stable.

Drino Zhao - 2021-03-23

The somber chinese substantively push because plywood maternally skip onto a grateful gratis rayon. wholesale, physical degree

Allen Zhang - 2020-12-23

Believe my classmech professor spent a whole week on this, smh

TackyLamb YT - 2020-10-08

I spent a whole 5 minutes flipping my phone after watching this video😂

S. Smith - 2019-09-20

Over 300 people broke their phone after watching this video.

Caroline Görtz - 2020-08-28

Must be the downvotes.

Vick Clash - 2020-09-01

😅😅😅

William R Buchanan - 2020-09-17

Dissapointing with no explanation of why it is happening in weightlessness of space, and no gravity. Only the energy of the spin to remove it from its thread. Free from thread and given an inertial instruction to use that energy until it was spent.you dont need a lot of a bump in space to send you on your way. It is giving its own instruction to intermittently flip about its centre of mass to reverse its motion. Since you can’t destroy energy, only give an equal and opposite to it by reversal of it, by itself, In space. My logic only, could be wrong, don’t fancy the maths. Diagrams.

꧁RadicalRick꧂ - 2020-10-03

I didn't break my smartphone after watching this video but that because it was already broken before doing this stunt.

jjstratford - 2020-10-04

Video sponsored by Apple

영하한 - 2021-03-23

The unknown sidecar natively watch because utensil logistically explode from a loud afternoon. woozy, sincere stick

jpdemer5 - 2020-09-28

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

Chris Wright - 2020-10-01

I could almsot imagine Feynman sitting forwards attentively with a smile on his face. The man had such a sense of humour and wonderful curiosity about the world.

kejdi Lleshi - 2020-10-02

Only for that phrase I disliked this video!

Chris Wright - 2020-10-02

@kejdi Lleshi why? I'm pretty sure Feynman would have loved to be proved wrong. Being proved wrong means you're learning something new, and from his books, that seems like something Feynman would have loved.

jpdemer5 - 2020-10-09

@Bruce E Schmidt Fixed!

jpdemer5 - 2020-10-09

@mr bottlespuller Of course he was aware of it... but he didn't think there was an easily-taught explanation. As a teacher, he'd have been delighted to find this.

ice cream - 2020-10-03

'The goal of this video is to prove Feynman wrong'
Me and the boys*
No pls dont humiliate him in front of us NO-

Noah Boddy - 2020-12-05

The space station in the motion picture '2001 : A Space Odyssey' would need to address this effect, don't you think? Not to mention the 'Discovery' spacecraft.

BC - 2019-09-19

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


Me: Rewatches again at .50x playback speed.

riskyrisk663 - 2020-09-10

After reading this comment, I watched it at 0.25x playback speed ... and realized for the first time that it makes the presenter sound really high! I recommend watching any scientific propositions at 1/4th speed - in fact, I highly recommend it (no pun intended).

riskyrisk663 - 2020-09-10

"The goal of this video, is to prove Feynman wrong" conveys the exact opposite of the intended message when played at 0.25x.

Aditya Saravanan - 2020-10-08

@Loredan13 there is no explanation on what creates the wobble. It cannot be created by itself due to the self correcting nature of gyroscopic effect

Andrew Sparkinson - 2021-01-28

@Bazof TheNorth hows about this for intuitive explanation, “ anything that can go wrong will go wrong eventually”..

Bazof TheNorth - 2021-01-28

@Andrew Sparkinson ha ha! Yes..more intuitive than the pronunciation of some of those Russian names!

teethendrikson - 2021-02-26

I noticed this weird dilemma way back when I tried to flip my flip-phone, and it never flipped like I wanted to

Gill Blondeel - 2021-03-03

As a dedicated skateboarder, I just found out how one does a proper hard flip.

David Borough - 2020-09-28

When I was a kid (playing tennis, 80's) I noticed this phenomenon (racquet) and always thought it was really cool. On rare occasion, I could get the racquet to flip without the 1/2 turn. But I didn't know there was SO MUCH more to it than "cool" :)

Phillip Alexander Carr - 2020-10-14

It’s micro thermals in organic vibration waves “clipping” the mass to flip it like a tennis ball bouncing in time on the racquet #roscosmos idea Mancuniancryptoguy

Alexander Saavedra - 2019-09-19

There is also a skateboard trick called the impossible flip because of this. They counter it by leading the front foot trough the flip to keep it from flipping on the other axis.

Tooba - 2019-09-20

@Jon Bowman wow u did.. I've been trying for so long☹️

melanieenmats - 2019-09-20

Oh he should make a video about that.

GameSpy DarkAge - 2019-09-20

Rodney Mullen defying the laws of physics since the 80s

Marco Arce - 2019-12-11

Exactly.... Mullen did this like 35 years ago.....on a board

Fred Hurst - 2020-08-29

I scrolled through comments to find if anyone mentioned this, I believe it was coined as the Impossible w/o the knowledge of why it is actually impossible from the physics standpoint. Still a good way to get a young skater more interested in physics.

James Armstrong - 2020-10-11

I feel headache, my neck is killing me, I can't turn, look, look at me.

Michael Markus Maurer - 2021-02-03

Thanks for the explanation. Leaving me with a question: I understand that the chance for a flip of earth is not given today due to the current distribution of mass on earth.
Remember the last ice age when ice masses had covered the poles. Would this different distribution of mass on earth increase the chance for a flip?
Can we calculate that different momentum?

Jarrell Prichard - 2021-03-04

Maybe why the magnetic poles switch every so often?

Be Like Water - 2021-03-08

They argue the poles move over 100,000s of years. Doesn’t our earth already wobble on its axis?

Garrett Ord - 2021-03-03

Interesting implication of this in the ability to flip celestial bodies just by moving a bit of mass around - relatively small amount of mass relative to the amount of thrust that would be required to force the same rotational change

ballparkjebusite - 2021-01-09

How would have plate tectonics change the earth’s moment of inertia over time (or will change it going into the future)?

Luis Breva - 2019-09-19

750 australians didnt like the fact Earth wont flip over.

Blue Eyes White Teddy - 2019-10-18

Why would they be mad? They're on top of the world.

野村ERIK - 2020-08-27

@The Free Philosopher I suspect this is wrong since the crust is an extremely small fraction of the Earth's overall mass. Also, beneath the crust is mantle and free-flowing liquid magma... So, it should mean mass distribution is relatively stable except for the bulge at the equator. If continents did have an effect, I imagine they would be exceedingly slight... I can see how you thought that, however, since from our perspective continents are massive.

Da Reproducer - 2020-09-01

@ArchEnema 67 It's a shame I can't see the look on your face when you read this >> They lied to you, child - Santa isn't real.

Da Reproducer - 2020-09-01

@Dinky-Di Hell yeah. Feel sorry for the Canadians... who really need to build a wall to keep those crazies locked out.

ArchEnema 67 - 2020-09-01

@Da Reproducer It's a shame I can't see the look on your face when I say this--Andrews will never allow Victorians out of their homes again: they're prisoners for life.😉

Tokanova - 2020-10-06

Could we flip the earth over by moving an excess of mass to, lets say, one of the hemispheres (northern or southern, whichever.) while taking it away from the equator?

michael jordan - 2021-02-15

Could we change the potion of the largest moment of inertia of Earth, with our technology, enough to cause it to make a sudden shift to the new greatest moment of inertia?

Aung Ko - 2020-10-05

I've been playing tennis since high school but I never noticed that so I just tried it and it actully spinned😱.

Gillanator - 2020-11-01

That's crazy I always wondered about this when flopping my phone. Thanks!

Gaswafers - 2019-09-20

The goal of this video is to prove Feynman wrong.
8 minutes left.

cinquine - 2019-09-23

@Telken Texas a -/-> b

Snarethedrummer - 2019-09-23

@BangDroid Here: It flips cause it's weighted equally and kinda funny, so it spins, then spins back. Full explanation? No. Intuitive? Yes. For a full explanation, rewatch the video (or video sections) until you do get it :P

Hebl von Heblowitz - 2019-10-03

Proving Feynman wrong is something that Feynman would approve of and even encourage.

skilz8098 - 2020-02-07

It's not hard to do; It's called thermodynamics and fluid dynamics with the path of least resistance along with angular momentum! Now the math behind it all is only partially trivial for there are too many partial derivatives and integrations by parts to take into consideration! You might want to brush up on your Linear Algebra with vector spaces, Euler angles, Affine Transformations and quaternions...

whatsthisidonteven - 2020-02-07

Super Metroid escape music starts playing in the background

Pip - 2020-10-09

I wish you could do an experiment to reverse the loss of grey cells, as mine have seemingly gone spinning in a path of least inertia, and in doing so flipped creating a black hole from whence they have disappeared..

Saqib Anjum Masoodi - 2021-03-10

When he said ''The greatest mathematician al."..... I literally shouted 'Terry Tao'....and I was correct. Credit goes to numberphile lmao😂.

Pale.Rider - 2020-10-08

Glad to know the Earth isn't gonna flip and fling us off, I thought I was about to develop a new phobia for a sec there

Kian Curatolo - 2020-11-05

Im curious, could something like this left to drift in empty space made out of a small crystal with the right properties, be considered a time crystal?