The Bizarre Behavior of Rotating Bodies, Explained

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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: ve42.co/LP
References:
Prof. Terry Tao's Math Overflow Explanation: ve42.co/Tao
The Twisting Tennis Racket
Ashbaugh, M.S., Chicone, C.C. & Cushman, R.H. J Dyn Diff Equat (1991) 3: 67. doi.org/10.1007/BF01049489
Janibekov’s effect and the laws of mechanics
Petrov, A.G. & Volodin, S.E. Dokl. Phys. (2013) 58: 349. doi.org/10.1134/S1028335813080041
Tumbling Asteroids
Prave et al. 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
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 NOburn 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.
Runtime: 14:48

Kommentarer

Frank Gavlak
Frank Gavlak - 3 timer siden
But the earth is NOT a perfect sphere; it's wider at the equator. Also, it is not a solid mass; it contains a fluid (molten) center core. Perhaps this core itself "flips" from time to time causing a reversing of the magnetic poles?
John Borden
John Borden - 7 timer siden
Would it be possible for CONTINENTAL DRIFT to change the earth's mass distribution sufficiently to destabilize it?
Joseph Chapes
Joseph Chapes - 16 timer siden
C
Bolerophon
Bolerophon - 17 timer siden
Feinman was right.
Jane
Jane - 23 timer siden
could this explain why gymnasts do the twists in the way they do?
matthew harris
matthew harris - Dag siden
All Homer Simpson heard was Bla, Bla, Blabla, bla. Oh & me too.
mj mia
mj mia - Dag siden
love math, good job
PimpleJThomas
PimpleJThomas - Dag siden
The Earth won't flip... Unless every human being on the planet, and every other living creature, and a bunch of tons and tons of organic and inorganic material, is massively brought up towards one of the poles: that would maybe change the Earth from spinning around the axis of maximum moment of inertia to just around the axis of intermediate moment of inertia, therefore it would flip, and flip again, and again...!
Aspect Aviation
Aspect Aviation - Dag siden
But in space how do the nut get the «shunt» to start the rotation?
Ajay Kumar
Ajay Kumar - Dag siden
I am from india
Leoni Benedetti
Leoni Benedetti - Dag siden
But why would the disk be bumped..? (8 min 27 s) Do we just assume that the small masses arent exactly on the y-axes?And thats why zentrifugal forces also appear there to make it flip...
Android480
Android480 - 2 dager siden
Intuitive is a stretch, but its damn good.
Mike Farmer
Mike Farmer - 2 dager siden
Learned this from a Carpenter back in sixties with a hammer...
Robert Boisvert
Robert Boisvert - 2 dager siden
Very cool. Curious if freezing or damning all the water to a high enough point could impact the Earth enough for a Dzhanibekov effect.
Nicco Saur
Nicco Saur - 2 dager siden
It’s unfortunate that he doesn’t know they are two different effects
Jonas Skanning
Jonas Skanning - 2 dager siden
does that mean before the earth was stabilized it actually flipped?
Saivivekh Swaminathan
Saivivekh Swaminathan - 2 dager siden
uh... you said 'intuitive explanation'... smh...
Hank Phillips
Hank Phillips - 2 dager siden
This explains polar shifting of planetary bodies as they move through space.
vikash gupta
vikash gupta - 2 dager siden
This might explain tilt of uranus
Chris Ralph
Chris Ralph - 2 dager siden
So the theory in the book "Down To A Sunless Sea" is wrong? The story goes that, in a nuclear war, if nuclear warheads detonate at the same point relative to the Earth's orbit, giving a large "nudge" to the Earth, precession will cause the Earth to tilt on its axis.
Legazonia
Legazonia - 2 dager siden
Yo guys, regarding this strange behavior and the earth, check out the declassified document called "The Adam and Eve Story"
Douglas Chitwood
Douglas Chitwood - 3 dager siden
Men!
Get ready 2 Get Funky.....
We About to be all one color!
Tops my day....
Rich Garella
Rich Garella - 3 dager siden
I know I'm out on a limb here, but I don't quite believe that this effect is causing the tennis racket (or phone) flip. The racket or phone flips immediately, every time, even though it is heavier than a wing nut. Well, your typical wing nut. Isn't it more likely that the tennis racket flip just results from our inability to send it up without spinning it a bit? If you try tumbling it with both hands you can make it flip without spinning. It's not easy though.
Douglas Chitwood
Douglas Chitwood - 3 dager siden
NICE! THANKA MON!
Jack hammer
Jack hammer - 3 dager siden
This is all fine and dandy, but, could we please do a follow up, if there already isn't one, that takes into consideration the magnetic fields and there influence
Jorge Chávez
Jorge Chávez - 3 dager siden
But could we put a giant nut at the north pole and it would turn right? lol
Michael Kendler
Michael Kendler - 3 dager siden
Isn’t the same argument with the centrifugal force also true for rotation around the max inertia axis...why is it stable?
SomeOne
SomeOne - 3 dager siden
So an old aged asteroid must spin at its axis of maximum moment of inertia...
And if it doesn't it must be recently created
SomeOne
SomeOne - 3 dager siden
1:58 I do that every single day yet never noticed it
SomeOne
SomeOne - 3 dager siden
This guy hits millions on every videos
Arch Stanton
Arch Stanton - 3 dager siden
You should flip it mechanically eliminate human imput
Jeff Byrer
Jeff Byrer - 3 dager siden
Why not just use a tennis racket
Sana omar
Sana omar - 3 dager siden
if we build something build or excavate some huge quantities of earth , for mining purposes ,of course . we could achieve such a disaster .
Grgazola
Grgazola - 3 dager siden
Shouldn't the explanation include the cause of small imbalances, the same as with the butterfly effect or other seemingly chaotic movements such as convection?
Michael Mills
Michael Mills - 3 dager siden
The Earth may BE STABLE, but you sir , are not...
Michael Mills
Michael Mills - 3 dager siden
I hate ppl who pronounce it " cent re "fuge" al' force! Aside from spelling its PRONOUNCED ' CENT TRIF I CAL' FORCE. EVERY AMERICAN AGREES.
Lucas Kman
Lucas Kman - 4 dager siden
Best Mathematician alive? You've not seen my maths teacher I guess.
Justin Credible
Justin Credible - 4 dager siden
BUT.... that's cgi... ;-)
Jishnu Rajeev
Jishnu Rajeev - 4 dager siden
I want earth to fcuking flip... Boring blue ball of water has done nothing cool yet
MARIN
MARIN - 4 dager siden
Finally the Earth will remain stable. Gosh! – I was so worried about that.
Joseph Caldwell
Joseph Caldwell - 4 dager siden
So in theory, if nothing ever "bumps" the object off the Y axis, this effect would not happen?
Emmanuel Lehuu
Emmanuel Lehuu - 4 dager siden
And if it never flips, thats proof the earth is round (more or less, my point being it isnt flat) so show this video to flat earthers ;)
Tatu Race 150
Tatu Race 150 - 5 dager siden
this disk has more 8 years, you video here
https://www.youtube.com/watch?v=tDr26U49_VA
Lerogi Z
Lerogi Z - 5 dager siden
Okay, okay. I’m finally watching it.
Daniel Loiselle
Daniel Loiselle - 5 dager siden
We’ll literally all flip out if global warming melts the ice caps..
Dre Mack
Dre Mack - 5 dager siden
All I could see was Booker T doing the Spinnerooni.
Roman Romero
Roman Romero - 5 dager siden
i wish my girlfriend wouldn't flip too 😂
Brad Cornwell
Brad Cornwell - 5 dager siden
Sooooooooo, does this mean that Arthur C Clarke's "Rama" wouldn't be possible?
Meow Milev
Meow Milev - 5 dager siden
Hmmmm i might introduce these to my new sling shot coaster!
Awreccan
Awreccan - 5 dager siden
8:24 but what causes the initial "bumping" of the disc that causes the small masses to lose alignment with the y axis?
DubDanTV
DubDanTV - 5 dager siden
0:48 Name of the movie?
Alethea Black
Alethea Black - 6 dager siden
Does anyone think that the wing nut, while attached to the screw, is *actually* magically flipping back and forth? This is a vivid testament to EMERGENCE THEORY; it supports the ground-breaking work of scientists such as Donald Hoffman and Klee Irwin, who argue for the brain's active involvement in *composing* what we see.
Jean Albus Persévérance
Jean Albus Persévérance - 6 dager siden
Exactly what I thought but much better verbalized, thanks for your explanation. :-)
Scott P
Scott P - 6 dager siden
Easy to see in real life. Flip a hammer. Done.
Konstantin Askinadze
Konstantin Askinadze - 6 dager siden
how would a tetraeder behave?
leohobb leohobb
leohobb leohobb - 6 dager siden
I think it is stupid and naive to trust passwords to a server company or web service.Last pass promoting is stupidity on nitro in my opinion.The rest of your video was ok with smart teori explained.
Caleb Cain
Caleb Cain - 6 dager siden
I have two questions about this, and maybe you, or somebody else reading these comments, would be able to answer them.
1. Out of curiosity, hypothetically, if the planet did flip, given the information you've explained, and the time it takes to complete one rotation along the normal axis of rotation (one day, of course.) how long would it take to flip?
2. What changes to the inertial points of the earth would occur if, let's somewhat less hypothetically say, we go from having a large mass of ice at each end to having a landmass at one end and ocean at the other with the ice distributed over the planet in the form of water?
I'll be honest, I'd love to tease out these questions myself, but I'm notoriously incompetent with higher math, and whatever I came up with would probably not be reliably accurate, even if I did manage to find an answer, so I thought I'd throw this out and see if anybody is more up to the task than I am.
Caleb Cain
Caleb Cain - 6 dager siden
SIde-note: I love your channel. Keep up the great work.
Alethea Black
Alethea Black - 6 dager siden
And here is the quote that describes it, by Lawrence M. Krauss: "But when you look at CMB map, you also see that the structure that is observed, is in fact, in a weird way, correlated with the plane of the earth around the sun. Is this Copernicus coming back to haunt us? That's crazy. We're looking out at the whole universe. There's no way there should be a correlation of structure with our motion of the earth around the sun - the plane of the earth around the sun - the ecliptic. That would say we are truly the center of the universe. The new results are either telling us that all of science is wrong and we're the center of the universe, or maybe the data is (s)imply incorrect, or maybe it's telling us there's something weird about the microwave background results and that maybe, maybe there's something wrong with our theories on the larger scales.”
Alethea Black
Alethea Black - 6 dager siden
The earth, the universe, indeed the multiverse routinely "flip." It is our perspective that is flipping. Here is the image of the Cosmic Microwave Background (CMB): https://arstechnica.com/science/2014/03/is-the-universe-lopsided/2/
Alethea Black
Alethea Black - 6 dager siden
This is brilliant. Thank you, Derek Muller. Whether the earth were to "actually flip" is a question inseparable from an observer. Indeed, there is substantial evidence from the Sloan Digital Sky Survey (SDSS) that the entire universe "flips" routinely along the ecliptic; see the alternating hot-and-cold pattern of the Cosmic Microwave Background (CMB), sometimes referred to as the "axis of evil" (because its implications could force us to rethink everything we believe we know about physics). Could centripetal and centrifugal forces, and the role of "an observer" have anything to do with human health? I explore this and more in my recent presentation (23-min) at the Science of Consciousness Conference. https://www.youtube.com/watch?v=dws-3gNzyZ4
Food Farm
Food Farm - 6 dager siden
Ok time to add more mass to the north pole
Matthew28 Apologetics
Matthew28 Apologetics - 6 dager siden
So what about an airplane propeller and its effect
Dennis G
Dennis G - 6 dager siden
I have seen this same effect with a kicked field goal (American football), look at the rotation and flip in slow motion, the laces rotate end over end as well....
Mans Ativo
Mans Ativo - 6 dager siden
Oh my i've been doing that on my phone cause it was cool. Flipping it then when I catch it, it faces backwards.
Chris Tashik
Chris Tashik - 6 dager siden
Very interesting. The Earth flipping idea reminds me of a spinning bowling ball. The internal core of a bowling ball is meant to make the ball “wobble” which allows for a different surface to contact the lane with each revolution. As someone who use to drill bowling balls for a living I know that with some lines and math this can be overcome and the ball can be drilled so that a specific user can roll it and the ball will rotate around only one axis. (Creating more or less hook)
SuperSupermario24
SuperSupermario24 - 6 dager siden
I would have appreciated it if you covered the other axes of rotation in the same way, showing why the same centrifugal forces wouldn't have been present in the other scenarios.
Achim Kandler
Achim Kandler - 6 dager siden
Hi, about the earth possibly being able to flip, your explanation that it behaves like an ateroid is not convincing. Look at the examples with the bottles filled with liquid. In the case of the earth it is also filled with liquid. And it has an atmosphere attached to it. With all these things together it looks to me it could flip. And we might already be in the very middle of it. The axis of the earth is tilted which is the reason we have seasons. Now this might or might not be connected. But I think it's too early to void the possibility it's happening to earth :-)
ameer hanani
ameer hanani - 7 dager siden
prophet muhammad said : "The Hour (the judgment day ) will not be established until the sun rises from the West. (6.158). Sahih al-Bukhari.
eppie design
eppie design - 7 dager siden
In balance !!
pkgfx.
pkgfx. - 7 dager siden
Who else just started flipping their phones??
Thomas Johnston
Thomas Johnston - 2 dager siden
Grabbed a book instead
Christopher Franko
Christopher Franko - 7 dager siden
He concludes the video with "the earth is spinning at its maximum moment of inertia which is stable" but.. the earth is changing. Ice caps are melting, land masses are moving.. couldnt the conditions change in a way that causes the flip one day?
Christopher Franko
Christopher Franko - 7 dager siden
As soon as I saw the object flipping i immediately thought "is earth going to do this one day?" and then my fears were allayed. 10/10 would watch again.
Ashwni Kumar
Ashwni Kumar - 7 dager siden
very interesting video
Pedro Viana
Pedro Viana - 7 dager siden
I wonder how much mass would need to be moved from the equator to the poles so as to change the axis with the maximum moment of inertia.
giuseppe d
giuseppe d - 7 dager siden
which tools have you used for animations?
DAY S
DAY S - 8 dager siden
In the quran 1400 yeats ago allah say the sun will rise from the sunset that time it doesn't matter if u become believer it's done
jalbert222
jalbert222 - 8 dager siden
I had to stop listening half way through. Cen tri FU gal forces? It is pronounced Cen TRI fi gal. Geeez.
jalbert222
jalbert222 - 6 dager siden
Good point and G'day :)
Stephen Parkinson
Stephen Parkinson - 8 dager siden
Not here matey. Two nations divided by a common language ;-)
Henry Henchion
Henry Henchion - 8 dager siden
So earth won’t flip bc it already flipped
Archangel Raphael
Archangel Raphael - 8 dager siden
so is the intermediate axis theorem an explanation for the *tippe top* that befuddled physicists like Pauli and Bohr?
https://kachina2012.wordpress.com/2008/04/14/chess-the-game-of-life-and-the-tippee-top/
Archangel Raphael
Archangel Raphael - 8 dager siden
AHA an anomaly that involves invoking centrifugal forces ... nice
Lorenzo Carelli apd
Lorenzo Carelli apd - 8 dager siden
This is the 4th time I am watching this, and finally I understand it
christopher welsh
christopher welsh - 8 dager siden
Years ago, I did once flip a tennis racket without it making that 1/2 turn. Once.
diecast jam
diecast jam - 8 dager siden
It could be called the remote control effect too. When I sit in bed watching TV I have a habit of flipping the remote control, and it always does this half rotation too, it's always intrigued me in a minor sort of way. I will try my best to not let it rotate by flipping it different ways, but no it still does the half rotation thing. Funny when I noticed it flipping the remote, I don't think it was that novel, I'm pretty sure it's something I have witnessed before in other things, probably the tennis racket.
cj valverde
cj valverde - 8 dager siden
This something stupid you would learn in school that has 0% help later in life
S Grim
S Grim - 8 dager siden
So earth, being partially liquid, will flip something approaching 90 degrees then.. (when the next ice-age puts enough ice-masses at the poles to force a flip towards the equator)
Jibran Saleem
Jibran Saleem - 8 dager siden
what if there was no disturbance at all in the intermediate axis as if it was spinning properly
Alex Ford
Alex Ford - 8 dager siden
Great video. I like intuitive answers rather than mathematic equations, etc., which I really do not trust regardless of how sophisticated their proofs. I love the intermediate, maximum moment and minimum moments of inertia. For some reason, this reminds me of Tesla, and I don't know why. AF
Thomas Kolb
Thomas Kolb - 8 dager siden
Hm, so this phenomenon is actually caused by the rotation not being perfectly aligned, but slightly bumped out of alignment. If the rotation was perfect (like mathematically perfect) it actually wouldn't happen. But in the real world, even the smallest (and I mean on a microscopic scale) misalignment will slowly accumulate and at some time (say, like after a million rotations) suddenly flip over to rotate yet another million rotations until the next flip... Interesting.
Justin Erickson
Justin Erickson - 8 dager siden
I learned two things that only bring on more questions. 1. Learned that spinning things in space are not necessarily stable. 2. Most people pronounce "centrifugal" force differently than this obviously very smart guy. Mind blown.
No Username
No Username - 9 dager siden
Is this why earth’s poles are moving?
Sergio Ontiveros
Sergio Ontiveros - 9 dager siden
Would it even matter if the earth flipped over? I mean would we even notice such an event? Or would the centrifugal force send anyone near the north and south pole flying into the sky? The reason i ask is because if i understand correctly, as the earth spins the surface can move at roughly 1600kmph and we dont seem to feel that, so if the earth suddenly flipped would we even notice it?
tiger12506
tiger12506 - 9 dager siden
Fascinating. So now I understand those toy tops that flip over when you spin them, or my phone which spins ok, but then violently wobbles, or why I am forced to anticipate the tennis racket flip. Really good video.
Dick Hansen
Dick Hansen - 9 dager siden
Love the way he explained this. So easy to understand.
BOBXFILES2374a
BOBXFILES2374a - 9 dager siden
Thank you, Professor Proton!!
BOBXFILES2374a
BOBXFILES2374a - 9 dager siden
This video keeps coming up i the sidebar. Much more interesting than I expected. The math, however, is nothing but meaningless squiggles to me!
Ls Sl
Ls Sl - 9 dager siden
How does that work with earth spinning
Nick Naccarato
Nick Naccarato - 9 dager siden
This video terrified me for a hot minute
raulsgomes
raulsgomes - 9 dager siden
Earth isnt going to flip if nothing interfers with its axis of inertia. But if something with a very big mass passes by.....
This is mass, but what about the change of the magnetosphere? Why does it happen?
Slim ben frej
Slim ben frej - 9 dager siden
In coran god tel . It s same day the sun rises in the west
Think you god for this religion
Dans le coran . Dieu dit . Que un jour la soleil se lève de l ouest
Merci dieux pou cette religion .
Peace for the humanity
La paix pour l humanité.
federico casabona
federico casabona - 9 dager siden
@veritasium, if humans decided to finally build the famous space elevator, so tall that would exit the orbit of the earth, would this elevator dissipate energy and eventually turn earth like happened with Explorer 1?
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