The Bizarre Behavior of Rotating Bodies, Explained

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  • 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.


  • Brady Patterson
    Brady Patterson  an hour ago

    So we're good here on earth, unless we decide to move all the heavy stuff to another axis? Lol

  • Gordon Schryer
    Gordon Schryer  2 hours ago

    with shifting techtonic plates and continental masses, clearly it hasn't always had those masses at the current equator - so its rotation must have been altered as the continental masses shift. Fortunately these things move somewhat slowly.

  • alexandra charles
    alexandra charles  2 hours ago

    Since bothering to sober up this time I have PROMISED myself to NEVER overestimate ANY other human being because it seems you are ALL AND I MEAN ALL a bunch of dunces!

  • alexandra charles
    alexandra charles  2 hours ago

    I must have been about 6 years old when I realised this and solved it.

  • eM Cee
    eM Cee  4 hours ago

    While your argument for why the Earth won't suddenly flip flop is convincing I would like to point out one discrepancy. As you noticed with the spinning containers with water on the inside, their moment of inertia is unstable and subject to erratic behavior along their intermediate axis.
    In turn, the Earth is filled with a liquid of sorts, molten magma, so i'm curious if any of that was factored into the models of how the Earth might eventually make a 180º pivot along its intermediate axis over vast expanses of deep time? If this does happen every so often could it be a logical mechanism for how the Earth repeatedly floods.. . as all the oceans of the world suddenly shift, submerging some land masses while exposing others that were previously flooded? A terrifying thought.

  • Konrad Comrade
    Konrad Comrade  5 hours ago

    or could Earth's rotation be flipped by building too much hydroelectric-dams, off at unsymmetric distances from the existing equator? Dams measurably do have an effect on the rpm of Earth! it is the first time since 4.5E9 years, that a (not so) advanced civilization is capable of doing so. The scientists of the USSR were possibly afraid of becoming obliged to dismantle their northern hydroelectric-dams!

  • Konrad Comrade
    Konrad Comrade  6 hours ago

    so what if: what if the ice-caps on the poles of a hyp.planet are growing, due to rapid climate change. Could such a fast change of moment of inertia overwhelm the energy-dissipation of the viscous, fluid interior or of a fluid equatorial ocean?

  • Leo Stanton Towne
    Leo Stanton Towne  6 hours ago

    If the earth were to flip over would we notice (other than by reference to the stars)?

  • Bizzaro World
    Bizzaro World  8 hours ago

    All of this to explain a wiggle???

  • Creepy ._. Creeper

    Doesn't it work on a spoon?

  • Nairda Charles
    Nairda Charles  8 hours ago

    I watched a girl twirking once, and she suddenly flipped ass over elbows. I thought she was just clumsy.

  • Clyde Kelvin and the Sinners.

    Hi there I find things like this fascinating. I made a little model with a molecular modeling kit that seems to have an odd stability when knocked over, it is a shape based upon the cuboctahedron. I was reading in Buzz Aldrin's book that this shape has interesting stability properties. I have a video of me knocking it over where it lands on one of the three outer weights whilst holding two thirds of the weight up in the air. I would love for you to tell me what you think is happening. If you look on my channel at the playlist labeled Things I do' The videos called Phfizzics Pah! and Physics Pah!
    I would love it if you would take a look and tell me what you think is causing it to have such stability, if you knock it too hard it falls over normally with two thirds of the outer weight down as it is only a plastic model. I hope you will take the time, thank you.

  • ke17h
    ke17h  9 hours ago

    well explained

  • --
    --  11 hours ago

    Einstein supported Crustal Displacement Theory, but also added the dynamic of melting polar ice, and the impact such redistribution of mass could have on the Earth’s centrifugal forces. Einstein supported it to the extent he penned a rare foreword to “Earth’s Shifting Crust,” published in 1958 and authored by Charles Hapgood. Full text, included. Enjoy.

  • CASPER 12345
    CASPER 12345  11 hours ago

    Ouch..........this video made my head hurt 😫

  • Prateek Panwar
    Prateek Panwar  11 hours ago

    YouTube showed me this thumbnail 1000 thousand times before clicking it

  • magebox
    magebox  13 hours ago

    But what about out huge magnetic earth center? Is this why we have pole shift?

  • nunya bidnezus
    nunya bidnezus  15 hours ago

    how do you know earth spins about the axis of greatest moment of enertia? wheres the proof of that?

  • Flynn1179
    Flynn1179  20 hours ago

    Just a thought.. would the melting of the polar icecaps cause water and hence mass to move towards the equator in accordance with centrifugal forces, resulting in the current axis no longer being that with the largest moment of inertia and hence flip the planet? Or would it make it MORE stable?

  • izzzzzz6
    izzzzzz6  21 hours ago

    V sauce. You missed out on this one!