A flip of the Earth on its axis

[arydberg]

TL;DR Summary

Spinning cue ball that flips

Does the Earth flip on its axis? I know the magnetic field will flip every 200,000 years or so but I am asking about the entire earth.

I have made a model of an Earth by drilling 2 perpendicular holes in a pool cue ball, filling them with lead and spinning it in a cushion of compressed air. It does flip back & forth and i have a movie but I do not know how to post it.

Any suggestions?

 

[Arjan82]

No, the Earth does not flip over its axis. This is a nice video about why flipping would occur:

 

[Arjan82]

I forgot, but it even explains why the Earth won't flip :)

 

[Leo Liu]

To the best of my knowledge, the axis of the Earth does not flip. However, the rotational axis of our planet is constantly changing due to the torque induced by the gravity forces. This motion is analogous to the precession of a top.

 

[arydberg]

Is there a way i can post a movie of the spinning ball fliping?

 

[Arjan82]

Upload it to youtube and provide the link?

 

[A.T.]

I have made a model of an Earth by drilling 2 perpendicular holes in a pool cue ball, filling them with lead

If you have messed around with the moments of inertia, then you might have created an unstable intermediate axis (see video below).

But why should that be a proper model of the Earth? What are you trying to emulate with your lead fillings? The Earth is not a rigid body like your ball. See the video in post #2, starting around 10:00.

 

[Halc]

Is there a way i can post a movie of the spinning ball fliping?

Your ball will flip because it is spinning on its axis of highest kinetic energy. You did this by filling the hole with lead. Try filling it with something lighter than the density of the ball. Then it is spinning with minimal kinetic energy like Earth does, and it will not flip.

The video explained all this.

The Earth is not a rigid body like your ball. See the video in post #2, starting around 10:00.

It also mistakenly depicts Earth reversing its angular momentum there, which is an error. The angular momentum of all the real objects and real simulations is unaltered in every other example.

 

[A.T.]

It also mistakenly depicts Earth reversing its angular momentum there, which is an error. The angular momentum of all the real objects and real simulations is unaltered in every other example.

Where exactly is the error? The angular momentum vector is constant in the inertial frame, but in the body-fixed frame (where the principal moments of inertia are defined) the angular momentum vector can flip over (when it's along the intermediate axis).

 

[Halc]

Where exactly is the error? The angular momentum vector is constant in the inertial frame ...

It IS constant in the inertial frame in every other example.
The T shaped object in the beginning and the wing nut both have constant angular momentum vector to the right both before and after the flip (despite the red arrow on the wing nut not following the angular momentum vector). Only the Earth example changes it, where it points up before, and down after, violating conservation of angular momentum. They just rotated a gif of the Earth spinning instead of giving it the motion of the (real) ball of clay shown seconds before.

 

[A.T.]

They just rotated a gif of the Earth spinning instead of giving it the motion of the (real) ball of clay shown seconds before.

Yes, at 10:13 in the Veritasium video, they simply 2D rotated the video clip of a spinning Earth, which is obvious from the fact that the illuminated side also changes. I guess since it's something that cannot happen anyway, they didn't bother to animate it "correctly". Likely they didn't do the 3D animation of the Earth themselves, just used some stock video clip.

 

[arydberg]

Upload it to youtube and provide the link?

I've done this before and got into trouble but will try again.

Thanks.

 

[James Demers]

The Earth is not rotating about an intermediate axis - like all celestial bodies, it's already rotating about it's most stable, highest-angular-momentum, lowest-kinetic-energy axis. To get it to flip, you'd have to get rid of the equatorial bulge, just for starters - and that's going to take a bit of energy.

 

[arydberg]

Here is a vidio i made

 

[Arjan82]

You need to go to settings and make this video public (it says the video is unavailable because it is private)

 

[arydberg]

You need to go to settings and make this video public (it says the video is unavailable because it is private)

I think i fixed it.

 

[A.T.]

I think i fixed it.

Log out from Google/Youtube. Then check if you can see it. If not, then it's still private.

 

[Arjan82]

Nope...

Go to your icon at the top right (the one with the letter, usually), then 'your channel', then 'manage videos'. There you should see all your videos. In the column 'Visibility' choose anything but private. On the options (hovering over the video, then the vertical link) you can get a sharable link.

 

[A.T.]

Here is a vidio i made

The axis through the smaller weights (marked blue and red) is the unstable intermediate axis:
https://en.wikipedia.org/wiki/Tennis_racket_theorem

But this doesn't apply to Earth (see video in post #2, starting around 10:00).

 

[DrStupid]

But this doesn't apply to Earth (see video in post #2, starting around 10:00).

But the argumentation in the video doesn’t apply to Earth either. It is correct, that non-rigid bodies tend to rotate around the axis that minimizes energy for the same angular momentum (due to dissipation of energy). However, that doesn’t matter if this axis is not fixed to the body. In case of Earth it is mainly the equatorial bulge that makes the axis stable (both by maximizing the moment of inertia and by interaction with the Moon). But the orientation of this bulge is defined by the axis of rotation.

If Earth would be tilted by let’s say 90° (whatever that means – see below), the bulge wouldn’t be tilted too. It would keep its orientation relative to the rotational axis and the rotational axis would remain in almost the same orientation because angular momentum is conserved and the moment of inertia tensor wouldn’t be significantly changed. That means that the effect, described in the video can't prevent Earth from flipping. If something like that would happen for some strange reason, Earth would always keep spinning around its most stable axis.

Another - even more general - problem is the definition of flipping for a partially liquid body. If the continental drift moves Antarctica to the North Pole and turns the other continents upside down, would that mean that Earth is flipped? If not, which conditions would need to be fulfilled in order to consider Earth to be flipped?

 

[A.T.]

But the argumentation in the video doesn’t apply to Earth either. It is correct, that non-rigid bodies tend to rotate around the axis that minimizes energy for the same angular momentum (due to dissipation of energy). However, that doesn’t matter if this axis is not fixed to the body. In case of Earth it is mainly the equatorial bulge that makes the axis stable (both by maximizing the moment of inertia and by interaction with the Moon). But the orientation of this bulge is defined by the axis of rotation.

If Earth would be tilted by let’s say 90° (whatever that means – see below), the bulge wouldn’t be tilted too. It would keep its orientation relative to the rotational axis and the rotational axis would remain in almost the same orientation because angular momentum is conserved and the moment of inertia tensor wouldn’t be significantly changed. That means that the effect, described in the video can't prevent Earth from flipping. If something like that would happen for some strange reason, Earth would always keep spinning around its most stable axis.

Another - even more general - problem is the definition of flipping for a partially liquid body. If the continental drift moves Antarctica to the North Pole and turns the other continents upside down, would that mean that Earth is flipped? If not, which conditions would need to be fulfilled in order to consider Earth to be flipped?

I agree. Using a rigid body as a model of the Earth fails on many levels here.

 

[arydberg]

I agree. Using a rigid body as a model of the Earth fails on many levels here.

I wonder how the spinning wing nut knows how long to to wait between flips. What determines the timing.

 

[A.T.]

I wonder how the spinning wing nut knows how long to to wait between flips. What determines the timing.

Instability means that small perturbations can cause a flip. The ellipsoid explanation shows an isolated system, where angular momentum and energy are conserved. But in reality you have some external torques, and energy dissipation. So neither quantity is strictly conserved and the ellipsoids and their intersection (the set of allowed rotation axes) are changing over time.

 

[arydberg]

"Instability means that small perturbations can cause a flip. " Where does the instability come from?

"The ellipsoid explanation shows an isolated system, where angular momentum and energy are conserved."
I agree

"But in reality you have some external torques, and energy dissipation". Where does the torgue come from?
What causes the energy to dissipate.

 

[A.T.]

Where does the instability come from? Where does the torgue come from?

It's not an ideal isolated system. It doesn't start out rotating exactly around the intermediate axis and it interacts with the air.

 

[Swamp Thing]

Here is a vidio i made
-- media --

Hi... a couple of weeks ago I spent some time floating a table tennis ball on a cushion of air and spinning it. Then I managed to attach some masses to the inner surface, such that there would be three different moments of inertia.

The result was that it would refuse to spin for much time on any axis except the one with the highest MoI. But I could not achieve the flipping-back-and-forth effect, and I had to put this project aside because of other stuff.

My question is, do you need to release the ball in a particular way in order to get the flipping effect? My guess was that I would have to do that -- and I was planning to make a pincer like device in which I could pre-spin the ball around its intermediate axis, before releasing it onto the air cushion.

Anyway, congratulations on this fine demonstration!

 

[A.T.]

Hi... a couple of weeks ago I spent some time floating a table tennis ball on a cushion of air and spinning it. Then I managed to attach some masses to the inner surface, such that there would be three different moments of inertia.

The result was that it would refuse to spin for much time on any axis except the one with the highest MoI. But I could not achieve the flipping-back-and-forth effect, and I had to put this project aside because of other stuff.

One idea: A table tennis ball is very light, so the air friction influences it much more, than denser objects.

 

[Swamp Thing]

One idea: A table tennis ball is very light, so the air friction influences it much more, than denser objects.

That's a good point. However, even an unloaded TT ball spins for nearly 30 seconds... so one might hope that the flipping would also persist for 10 seconds at least, if we're able to induce it somehow in the first place. Unless the damping affects the flipping to a MUCH higher degree for some reason.

In the wing-nut example, the nut is constrained to spin on the intermediate axis as long as it's running on the bolt -- and then it's free to do its thing from that point. My thinking is that we need to replicate that -- but ARydberg already knows the secret

 

[A.T.]

That's a good point. However, even an unloaded TT ball spins for nearly 30 seconds... so one might hope that the flipping would also persist for 10 seconds at least, if we're able to induce it somehow in the first place. Unless the damping affects the flipping to a MUCH higher degree for some reason.

I cannot say more without specifics of the experiment. But as explained in this thread and the video: If you have substantial energy dissipation, then only the maximal MoI-axis is stable.

See around 11:20:

 

[arydberg]

Hi... a couple of weeks ago I spent some time floating a table tennis ball on a cushion of air and spinning it. Then I managed to attach some masses to the inner surface, such that there would be three different moments of inertia.

The result was that it would refuse to spin for much time on any axis except the one with the highest MoI. But I could not achieve the flipping-back-and-forth effect, and I had to put this project aside because of other stuff.

My question is, do you need to release the ball in a particular way in order to get the flipping effect? My guess was that I would have to do that -- and I was planning to make a pincer like device in which I could pre-spin the ball around its intermediate axis, before releasing it onto the air cushion.

Anyway, congratulations on this fine demonstration!

The ball has a 1/4 inch hole drilled through and filled with lead. Then a 1/8 inch hole is drilled at right angles to the other hole and filled with lead. To answer your question the ball needs to be spun about the 1/8 inch hole.

Also on the subject of table tennis balls if you weight one half of the ball. by spliting it in two, filling one half with epoxy and glueing it back together and color the weighted half it sits with the weighted half down but when spun it will flip. It is stable when spinning only with the weighted half on top. You can also drill a hole in the ball, half fill it with water. and freeze it and color the weighted half. It workes fine for a short time till the water melts.

 

[Swamp Thing]

Thanks for the info!

 

[A.T.]

Also on the subject of table tennis balls if you weight one half of the ball. by spliting it in two, filling one half with epoxy and glueing it back together and color the weighted half it sits with the weighted half down but when spun it will flip. It is stable when spinning only with the weighted half on top. You can also drill a hole in the ball, half fill it with water. and freeze it and color the weighted half. It workes fine for a short time till the water melts.

What is the spin axis with respect to the halves?

The half filled balls give you no clear intermediate axis. And your center of mass is not the ball center, so you have substantial external torques around the CoM from the air cushion support. This is likely quite different from the typical intermediate axis flipping.

 

[Swamp Thing]

In order to get the most intriguing demo, is it better to have the three principal MoIs fairly close to each other, or is it better if they are as different as possible?