The Bizarre Behavior of Rotating Bodies, Explained

19 sept. 2019
6 951 343 Vues

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 FRlift 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.

Commentaires
  • I don't know if you read these comments, but I hope you read mine. I'm only going to make one point. When you spin a basketball and balance it on your fingertip, it causes a torsional rotation force that you have to actively compensate for to maintain its balance!!!

    Albert Bourgeois, D.O.Albert Bourgeois, D.O.Il y a 24 minutes
  • my stomach sober = 1 axis my stomach absolutely hammered = 3 axes

    MarcelloMarcelloIl y a 32 minutes
  • 9:19 if the centrifugal force is proportional to 1/r^2 so if the distance from Y-axis increases then the force centrifugal force decreases so how the lighter mass accelerates when it is going far from Y-axis

    Warrior ##Warrior ##Il y a 15 heures
  • Why did he lie? The Earth's distribution of mass is constantly changing because of the tides primarily caused by the Moon at an angle not 90 degrees from the axis of rotation. The Earth is tilted. Plus human-induced climate change is causing the heating of the Earth in it's entirety, not just the atmosphere. This causes the liquid core that surrounds the solid core to become less viscous. This allows the solid core to be moved more by the influence of the Moon.

    rodgersericvrodgersericvIl y a 19 heures
  • You showed some evidence that mars is rotating on its third axis, and then didn’t do the same for earth. You literally just asserted it and then moved on. Looking at the North American Craton, you might want to do more than just assert what you hope for.

    New Tunes For Old LogosNew Tunes For Old LogosIl y a jour
  • Its possible to make an zero gravity engine with magnetic superposition against centrifugal force of the body of the engine to propel forward. To achive this, minimum 4500RPM rotating coil againt superconductor; increasing acceleration of any typical fuel driven engine upto 70times.

    Anirban Joarder TonmoyAnirban Joarder TonmoyIl y a jour
  • Flat Earthers have been flipping since the Earth was formed.

    Paras PathejaParas PathejaIl y a jour
  • My pocketknife does that! I only nitice because there's a safety on one side

    Smitty Cruze And The DropoutsSmitty Cruze And The DropoutsIl y a jour
  • immanuel Velkovsky, in his book "Earth in Upheaval" has tried to prove that earth does flip after every around 20,000 years. He proved this point by showing the layers of coral deposits on seabed. A column of coral sediment pulled out for research, showed that polarity of coral deposits changed suddenly, corresponding to 20k years of earth. According to him, the next flip is around the corner. (he died in 1979)

    airman3airman3Il y a jour
  • I lost you at 7 minute mark.

    Mohammad SagorMohammad SagorIl y a jour
  • My dude.. you are crazy smart. Thanks for sharing your knowledge with everyone!

    TimTimIl y a 3 jours
  • And with all of the satellites around the earth, the hubble telescope, the supposed space stations we still do not have anything but NASA art of things happening supposedly in orbit around the earth.

    Suzanne HartmannSuzanne HartmannIl y a 4 jours
  • This vid has me flipping crap all morning long.

    Ivan DenisovichIvan DenisovichIl y a 4 jours
  • But what about our binary or a trinary star, that's a very dense, white dwarf star that is dark and can only be seen with an infrared telescope, such as Lucifer. When this highly dense white dwarf comes through our solar system on an elliptical orbit, it could possibly cause our planet to pole shift among other things. And there is always the flat earth hypothesis that includes living under a dome firmament, and Antarctica is actually a barrier before the dome. And the the Holographic universe theory, as we are most probably existing in a holographic simulator, being ignorant to the illusion thinking everything is real and solid. Thank you for the excellent video!

    Loren Seditious SenseiLoren Seditious SenseiIl y a 5 jours
  • 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?

    Frank GavlakFrank GavlakIl y a 6 jours
  • Would it be possible for CONTINENTAL DRIFT to change the earth's mass distribution sufficiently to destabilize it?

    John BordenJohn BordenIl y a 6 jours
  • C

    Joseph ChapesJoseph ChapesIl y a 6 jours
  • Feinman was right.

    BolerophonBolerophonIl y a 6 jours
  • could this explain why gymnasts do the twists in the way they do?

    JaneJaneIl y a 6 jours
  • All Homer Simpson heard was Bla, Bla, Blabla, bla. Oh & me too.

    matthew harrismatthew harrisIl y a 7 jours
  • love math, good job

    mj miamj miaIl y a 7 jours
  • 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...!

    PimpleJThomasPimpleJThomasIl y a 7 jours
  • But in space how do the nut get the «shunt» to start the rotation?

    Aspect AviationAspect AviationIl y a 7 jours
  • I am from india

    Ajay KumarAjay KumarIl y a 7 jours
  • 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...

    Leoni BenedettiLeoni BenedettiIl y a 7 jours
  • Intuitive is a stretch, but its damn good.

    Android480Android480Il y a 7 jours
  • Learned this from a Carpenter back in sixties with a hammer...

    Mike FarmerMike FarmerIl y a 8 jours
  • Very cool. Curious if freezing or damning all the water to a high enough point could impact the Earth enough for a Dzhanibekov effect.

    Robert BoisvertRobert BoisvertIl y a 8 jours
  • It’s unfortunate that he doesn’t know they are two different effects

    Nicco SaurNicco SaurIl y a 8 jours
  • does that mean before the earth was stabilized it actually flipped?

    Jonas SkanningJonas SkanningIl y a 8 jours
  • uh... you said 'intuitive explanation'... smh...

    Saivivekh SwaminathanSaivivekh SwaminathanIl y a 8 jours
  • This explains polar shifting of planetary bodies as they move through space.

    Hank PhillipsHank PhillipsIl y a 8 jours
  • This might explain tilt of uranus

    vikash guptavikash guptaIl y a 8 jours
  • 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.

    Chris RalphChris RalphIl y a 8 jours
  • Yo guys, regarding this strange behavior and the earth, check out the declassified document called "The Adam and Eve Story"

    LegazoniaLegazoniaIl y a 8 jours
  • Men! Get ready 2 Get Funky..... We About to be all one color! Tops my day....

    Douglas ChitwoodDouglas ChitwoodIl y a 9 jours
  • 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.

    Rich GarellaRich GarellaIl y a 9 jours
  • NICE! THANKA MON!

    Douglas ChitwoodDouglas ChitwoodIl y a 9 jours
  • 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

    Jack hammerJack hammerIl y a 9 jours
  • But could we put a giant nut at the north pole and it would turn right? lol

    Jorge ChávezJorge ChávezIl y a 9 jours
  • Isn’t the same argument with the centrifugal force also true for rotation around the max inertia axis...why is it stable?

    Michael KendlerMichael KendlerIl y a 9 jours
  • 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

    SomeOneSomeOneIl y a 9 jours
  • 1:58 I do that every single day yet never noticed it

    SomeOneSomeOneIl y a 9 jours
  • This guy hits millions on every videos

    SomeOneSomeOneIl y a 9 jours
  • You should flip it mechanically eliminate human imput

    Arch StantonArch StantonIl y a 9 jours
  • Why not just use a tennis racket

    Jeff ByrerJeff ByrerIl y a 9 jours
  • if we build something build or excavate some huge quantities of earth , for mining purposes ,of course . we could achieve such a disaster .

    Sana omarSana omarIl y a 9 jours
  • 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?

    GrgazolaGrgazolaIl y a 9 jours
  • The Earth may BE STABLE, but you sir , are not...

    Michael MillsMichael MillsIl y a 9 jours
  • I hate ppl who pronounce it " cent re "fuge" al' force! Aside from spelling its PRONOUNCED ' CENT TRIF I CAL' FORCE. EVERY AMERICAN AGREES.

    Michael MillsMichael MillsIl y a 9 jours
  • Best Mathematician alive? You've not seen my maths teacher I guess.

    Lucas KmanLucas KmanIl y a 10 jours
  • BUT.... that's cgi... ;-)

    Justin CredibleJustin CredibleIl y a 10 jours
  • I want earth to fcuking flip... Boring blue ball of water has done nothing cool yet

    Jishnu RajeevJishnu RajeevIl y a 10 jours
  • Finally the Earth will remain stable. Gosh! - I was so worried about that.

    MARINMARINIl y a 10 jours
  • So in theory, if nothing ever "bumps" the object off the Y axis, this effect would not happen?

    Joseph CaldwellJoseph CaldwellIl y a 10 jours
  • 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 ;)

    Emmanuel LehuuEmmanuel LehuuIl y a 10 jours
  • this disk has more 8 years, you video here frlift.info/first/vid-o/2XrVmJqHlnHEiHo.html

    Tatu Race 150Tatu Race 150Il y a 10 jours
  • Okay, okay. I’m finally watching it.

    Lerogi ZLerogi ZIl y a 11 jours
  • We’ll literally all flip out if global warming melts the ice caps..

    Daniel LoiselleDaniel LoiselleIl y a 11 jours
  • All I could see was Booker T doing the Spinnerooni.

    Dre MackDre MackIl y a 11 jours
  • i wish my girlfriend wouldn't flip too 😂

    Roman RomeroRoman RomeroIl y a 11 jours
  • Sooooooooo, does this mean that Arthur C Clarke's "Rama" wouldn't be possible?

    Brad CornwellBrad CornwellIl y a 11 jours
  • Hmmmm i might introduce these to my new sling shot coaster!

    Meow MilevMeow MilevIl y a 11 jours
  • 8:24 but what causes the initial "bumping" of the disc that causes the small masses to lose alignment with the y axis?

    AwreccanAwreccanIl y a 11 jours
  • 0:48 Name of the movie?

    DubDanTVDubDanTVIl y a 11 jours
  • 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.

    Alethea BlackAlethea BlackIl y a 12 jours
  • Exactly what I thought but much better verbalized, thanks for your explanation. :-)

    Jean Albus PersévéranceJean Albus PersévéranceIl y a 12 jours
  • Easy to see in real life. Flip a hammer. Done.

    Scott PScott PIl y a 12 jours
  • how would a tetraeder behave?

    Konstantin AskinadzeKonstantin AskinadzeIl y a 12 jours
  • 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.

    leohobb leohobbleohobb leohobbIl y a 12 jours
  • 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 CainCaleb CainIl y a 12 jours
    • SIde-note: I love your channel. Keep up the great work.

      Caleb CainCaleb CainIl y a 12 jours
  • 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 BlackAlethea BlackIl y a 12 jours
  • 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): arstechnica.com/science/2014/03/is-the-universe-lopsided/2/

    Alethea BlackAlethea BlackIl y a 12 jours
  • 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. frlift.info/first/vid-o/ya3Wk5eZsLLejG0.html

    Alethea BlackAlethea BlackIl y a 12 jours
  • Ok time to add more mass to the north pole

    Food FarmFood FarmIl y a 12 jours
  • So what about an airplane propeller and its effect

    Matthew28 ApologeticsMatthew28 ApologeticsIl y a 12 jours
  • 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....

    Dennis GDennis GIl y a 12 jours
  • Oh my i've been doing that on my phone cause it was cool. Flipping it then when I catch it, it faces backwards.

    Mans AtivoMans AtivoIl y a 12 jours
  • 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)

    Chris TashikChris TashikIl y a 12 jours
  • 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.

    SuperSupermario24SuperSupermario24Il y a 12 jours
  • 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 :-)

    Achim KandlerAchim KandlerIl y a 12 jours
  • prophet muhammad said : "The Hour (the judgment day ) will not be established until the sun rises from the West. (6.158). Sahih al-Bukhari.

    ameer hananiameer hananiIl y a 13 jours
  • In balance !!

    eppie designeppie designIl y a 13 jours
  • Who else just started flipping their phones??

    pkgfx.pkgfx.Il y a 13 jours
    • Yep I did for like 5 minutes and it always twists.

      aforementioned dudeaforementioned dudeIl y a 22 heures
    • Grabbed a book instead

      Thomas JohnstonThomas JohnstonIl y a 8 jours
  • 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 FrankoChristopher FrankoIl y a 13 jours
  • 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.

    Christopher FrankoChristopher FrankoIl y a 13 jours
  • very interesting video

    Ashwni KumarAshwni KumarIl y a 13 jours
  • 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.

    Pedro VianaPedro VianaIl y a 13 jours
  • which tools have you used for animations?

    giuseppe dgiuseppe dIl y a 13 jours
  • 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

    DAY SDAY SIl y a 14 jours
  • I had to stop listening half way through. Cen tri FU gal forces? It is pronounced Cen TRI fi gal. Geeez.

    jalbert222jalbert222Il y a 14 jours
    • Good point and G'day :)

      jalbert222jalbert222Il y a 12 jours
    • Not here matey. Two nations divided by a common language ;-)

      Stephen ParkinsonStephen ParkinsonIl y a 14 jours
  • So earth won’t flip bc it already flipped

    Henry HenchionHenry HenchionIl y a 14 jours
  • so is the intermediate axis theorem an explanation for the *tippe top* that befuddled physicists like Pauli and Bohr? kachina2012.wordpress.com/2008/04/14/chess-the-game-of-life-and-the-tippee-top/

    Archangel RaphaelArchangel RaphaelIl y a 14 jours
  • AHA an anomaly that involves invoking centrifugal forces ... nice

    Archangel RaphaelArchangel RaphaelIl y a 14 jours
  • This is the 4th time I am watching this, and finally I understand it

    Lorenzo Carelli apdLorenzo Carelli apdIl y a 14 jours
  • Years ago, I did once flip a tennis racket without it making that 1/2 turn. Once.

    christopher welshchristopher welshIl y a 14 jours
  • 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.

    diecast jamdiecast jamIl y a 14 jours
  • This something stupid you would learn in school that has 0% help later in life

    cj valverdecj valverdeIl y a 14 jours
  • 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)

    S GrimS GrimIl y a 14 jours
  • what if there was no disturbance at all in the intermediate axis as if it was spinning properly

    Jibran SaleemJibran SaleemIl y a 14 jours
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