The Bizarre Behavior of Rotating Bodies, Explained

  • Published on:  Thursday, September 19, 2019
  • 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:

    Prof. Terry Tao's Math Overflow Explanation:

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

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

    Tumbling Asteroids
    Prave et al.

    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.
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  • James Beemer

    James Beemer

     an hour ago

    The Soviet Union made it secret because of the gyro . Guidence systems .

  • James Beemer

    James Beemer

     an hour ago

    He's talking math , in combination with physics .

  • James Beemer

    James Beemer

     an hour ago

    Zero G is ideal to watch as it happen .

  • Vance Fearon

    Vance Fearon

     3 hours ago

    That is the consequence of the Earth being an oblate spheroid, Earth will continue spinning with the widest part at the equator, hooray.

  • cmdr lee

    cmdr lee

     4 hours ago

    Ask any electrian when they flips their linemen plyers around the same effect



     5 hours ago

    What about the core in liquid, will that flip. Is that why we a are in a start of a  magnetic reversal ?

  • Yours Truely

    Yours Truely

     8 hours ago +1

    The earth is not round its wider in the middle

  • Uzair Ali

    Uzair Ali

     8 hours ago +1

    damm, did this with my phone, was in such awe i forgot to catch it. now its at the bottom of a drain. :( RIP

  • iTs Inulater

    iTs Inulater

     9 hours ago +1

    I'm not going to lie.. This video had me clenching and holding my breath. But still, a lot more experiments could be done. Like the effects of an orbiting object. Or with different liquid densities. Great Videos.

  • SwaffyX


     9 hours ago +1

    I understood what you were saying, and it actually makes sense. This planet (Earth) isn't perfectly round. The mass is off just enough to keep it stabily rotating, hence our equator. And why we have arctic zones near the poles.

  • Johannes


     10 hours ago +1

    Sooo.... If we thaw Mars's ice..... It will change its rotation?

  • Ringo Schubert

    Ringo Schubert

     11 hours ago +1

    The Earth is spinning around it's axis with the maximum amount of inertia, but is this axis slowly shifting with continental drift?

  • Skyclad


     11 hours ago +1

    Anyone not sure why the wing nut still flips after being stabilized by the bolt, I have an explanation: At the very end of the bolt, where the thread terminates, is a single point where the thread is flush with the end of the bolt. 180 degrees away from that, it is not. So as the wing nut reaches the end, there is a moment right before the wing nut frees itself completely that the thread is applying force to only part of the wing nut. This uneven force just as it makes that last turn off the bolt, induces a slight wobble.
    You can see this in the video.

  • Mike Hari

    Mike Hari

     23 hours ago +1

  • Bradley Moriarty

    Bradley Moriarty


    I work in a kitchen and have always wondered why flipping my tongs from the base, it always did a 180 turn. thank you!

  • Mark GB

    Mark GB

     yesterday +1

    Stable until the land masses change due to subduction, and then whoops

  • RaysGolfCartsColumbus


     yesterday +1

    I can find you at least a dozen carpenters that knew of this phenomenon way before 1989 and it is called the law of the hammer... When you hold a claw hammer by the handle and give it flip, the hammer head will change sides once for each revolution... This isn't a Russian secret lol...

  • Panshul Saxena

    Panshul Saxena


    Aag laga diye ho bhai 🔥🔥🔥🔥

  • Shashwat Poudel

    Shashwat Poudel


    You flipped your phone, didn't you?

  • karan mehra

    karan mehra


    I discovered everything when I was a kid.. . But i never knew the science behind it