Spooky Rotations

[Gun Nut]

When a Russian Astronaut aboard their space station spun a wingnut off of a bolt in zero gravity, something very strange happened.
The bolt continued to spin weightlessly for a few seconds... and then it spontaneously flipped over, 180 degrees, and continued to spin. It then flipped over again on its own, and continued to spin... and spun, and spun, continuously flipping over every few seconds.
It was so strange looking, and unexpected, the Russians kept the (totally repeatable) observation a secret for 10 years.

Little did they know, the Americans already knew all about this particular phenomenon.. It's called "The Tennis Racket Theorem".. otherwise known as the "Intermediate Axis Theorem". It goes like this...

Any body with mass that has 3 different moments of inertia (a maximum, a minimum, and an intermediate) will behave this way...
If you rotate the body around either axis of it's maximum or minimum inertia, then nothing special happens. It spins as expected.
If you attempt to rotate the body around its intermediate axis, the body will also spontaneously rotate around it's axis of minimum inertia.

This is easily demonstrated with a tennis racket;
If you hold the racket out in front of you, like you were about to return a serve, and spin it in the air with a twist of the wrist, you will be spinning it along it's axis of minimum inertia.. and it will just spin as expected. Likewise, if you are holding the racket out in front of you, and spin it like a platter, with one face pointing upward and the other pointing downward at all times, then you will be spinning it along it's axis of maximum inertia. Again, nothing special happens.
BUT... try and "flip" it... spin it along it's intermediate axis, like you were tossing the racket into the air and catching it again after the handle rotates away and back into your hand.. something odd happens... it "twists"... or rather, also rotates along its minimum axis... no matter what you do or how you attempt to rotate it.
There is no stopping it. It is impossible to flip a tennis racket without it also spontaneously "twisting" in the air.

Can anybody:

a) explain why this happens and how one could predict when it flips over

b) propose a novel way to exploit this behavior for Good(TM)? Or identify where this has been used in engineering or whatever to solve a problem...

 

[repoman]

There was a good explanation on the Veritasium channel. But I suggest to think about this on your own before watching it.

 

[skepticalbip]

It was an example of a really old physics observation. When I was a physics student back in the 1970s there was a popular jabberwockian sounding expression among physics students, "The herpolhode holds and the polhode rolls in the invariable plane without slipping". It describes a phenomena that a body rotating about a minor axis will create an astable condition for another axis. The flip can't really be predicted exactly because it is from an instability... sorta like it is known that a pyramid balanced on its tip with the base in the air will fall over because that is an astable condition but how long it will take before it falls over is unpredictable.

ETA:
OOPS... I missed this question:

b) propose a novel way to exploit this behavior for Good(TM)?

It depends on how you define "good". If this means making a profit then that is easily done. Bet someone that they can't hold a hammer with the peen to the right and the claw to the left then flip it a full 360 degrees about that axis and catch it with the peen still pointing to the right. Well over 99% of the time the peen will be pointing in the opposite direction than it started after a full 360 degree flip of the handle.

 

[steve_bank]

The Russians apparently had a number of spooky experiences out there.

Sounds like this. Imagine a disk where there are multiple high density spots. It is unbalanced. Move it with a vector while it is spinning and it can go any number of ways.

Causal but unpredictable. Chaos theory?

 

[Shadowy Man]

There was a good explanation on the Veritasium channel. But I suggest to think about this on your own before watching it.

I saw that video recently. I recommend it as well.

 

[Gun Nut]

The videos I saw showed objects "flipping" at very regular intervals. Yet those intervals are indeterminate? Or just too complicated to predict? What, then, keeps them regular?

 

[repoman]

This is the video I was referring to.

 

[skepticalbip]

The videos I saw showed objects "flipping" at very regular intervals. Yet those intervals are indeterminate? Or just too complicated to predict? What, then, keeps them regular?

Constant rate of rotation and unvarying distribution of mass should mean that the almost same amount of time would be needed for the destabilizing forces to mount up enough to cause a flip to the other metastable position. Spin it slower or faster or another object with different mass distribution should result in a different time interval between flips.

 

[beero1000]

The videos I saw showed objects "flipping" at very regular intervals. Yet those intervals are indeterminate? Or just too complicated to predict? What, then, keeps them regular?

They are not indeterminate or unpredictable. As long as you know the moments of inertia and the initial rotational velocities you can predict the flipping period by solving Euler's equations.

 

[Treedbear]

The videos I saw showed objects "flipping" at very regular intervals. Yet those intervals are indeterminate? Or just too complicated to predict? What, then, keeps them regular?

They are not indeterminate or unpredictable. As long as you know the moments of inertia and the initial rotational velocities you can predict the flipping period by solving Euler's equations.

Maybe you'd know then. Does the flip need to completely occur during a single rotation?

ETA -
Another thing. While the angular momentum of the entire structure remains the same, it looks like the angular momentum of each individual particle of the structure reverses during the flip. It seems that during the flip the total angular momentum around the principle axis of rotation is shifted by 90 degrees and then another 90. But at the midpoint it equals zero.

It would be neat to have a laser at the central axis so the beam flips directions. I wonder if this could be similar to what occurs with pulsars.

 

[skepticalbip]

... snip ...


It would be neat to have a laser at the central axis so the beam flips directions. I wonder if this could be similar to what occurs with pulsars.

My understanding of the current model for pulsars is that the highly directional beam of radiation is emitted from both the north and south poles of a rapidly spinning neutron star. A precession of the axis makes the beams sweep in circles. We see a 'pulse' when the direction of that circling beam sweeps past us.

But then I or that model could be wrong.

 

[beero1000]

The videos I saw showed objects "flipping" at very regular intervals. Yet those intervals are indeterminate? Or just too complicated to predict? What, then, keeps them regular?

They are not indeterminate or unpredictable. As long as you know the moments of inertia and the initial rotational velocities you can predict the flipping period by solving Euler's equations.

Maybe you'd know then. Does the flip need to completely occur during a single rotation?

ETA -
Another thing. While the angular momentum of the entire structure remains the same, it looks like the angular momentum of each individual particle of the structure reverses during the flip. It seems that during the flip the total angular momentum around the principle axis of rotation is shifted by 90 degrees and then another 90. But at the midpoint it equals zero.

It would be neat to have a laser at the central axis so the beam flips directions. I wonder if this could be similar to what occurs with pulsars.

This thesis has a full analytic solution worked out. There's an interesting graph of the angular momentum components on page 24.

 

[Treedbear]

...
This thesis has a full analytic solution worked out. There's an interesting graph of the angular momentum components on page 24.

View attachment 24312

Fascinating. Thank you very much.

 

[Gun Nut]

The videos I saw showed objects "flipping" at very regular intervals. Yet those intervals are indeterminate? Or just too complicated to predict? What, then, keeps them regular?

They are not indeterminate or unpredictable. As long as you know the moments of inertia and the initial rotational velocities you can predict the flipping period by solving Euler's equations.

Would that be any "easier" than, say, using physics equations to predict the outcome of a throw of dice? Is this a "technically not random - but it's really pretty darn random" thing?

 

[Gun Nut]

I wonder if this could be similar to what occurs with pulsars.

Or Earth (!!!!!)

That video was good... Earth is already rotating along a stable axis, they say.

 

[beero1000]

The videos I saw showed objects "flipping" at very regular intervals. Yet those intervals are indeterminate? Or just too complicated to predict? What, then, keeps them regular?

They are not indeterminate or unpredictable. As long as you know the moments of inertia and the initial rotational velocities you can predict the flipping period by solving Euler's equations.

Would that be any "easier" than, say, using physics equations to predict the outcome of a throw of dice? Is this a "technically not random - but it's really pretty darn random" thing?

I would say it would be much easier than predicting the number of a roll of dice and maybe a bit harder than predicting the trajectory of a thrown ball. There definitely is a chaotic component to the unstable equilibrium, so the longer you let it go the less predictable it would be.