[Airthumbs (OP)]

We could also ask what would happen if the skater farted at the same time as she was pulling in her arms to make herself spin faster. However, that might only complicate things  []

The fastest spin on ice skates was achieved by Natalia Kanounnikova, with a maximum rotational velocity of 308 RPM at Rockefeller Centre Ice Rink, New York, USA on 27 March 2006. Maybe she has a secret, Geezer?

[JP]

What if the cows all actually ran along and all farted at the same time with their hooves touching the ground?  []

We could also ask what would happen if the skater farted at the same time as she was pulling in her arms to make herself spin faster. However, that might only complicate things  []

What if a cow ran by the skater and farted on her while she was spinning around in outer space?

[Geezer]

What if the cows all actually ran along and all farted at the same time with their hooves touching the ground?  []

We could also ask what would happen if the skater farted at the same time as she was pulling in her arms to make herself spin faster. However, that might only complicate things  []

What if a cow ran by the skater and farted on her while she was spinning around in outer space?

Didn't Feynman touch on that in one of his lectures?

[Bored chemist]

Unless you accept that the earth's atmosphere is part of the earth.

So, either there's no overall effect (provided that you don't think the atmosphere is part of the earth) or there's a temporary effect (which dies out rather rapidly).

Take your pick, but the idea that "It does not need to "keep going". The work was done, and that's all it takes to alter the state of the system." is wrong.

Incidentally cows generally burp more than they fart so the net effect would be the reverse of that predicted.

BC, what you are obviously failing to grasp is that the mass accelerated by the cows is a consequence of work done by chemical processes. Chemical energy was converted into kinetic energy, and added to the kinetic energy of the system as a whole.

Not only have I grasped it, I have understood the consequence of it.I also understood that the kinetic energy is rapidly converted to heat by friction within the atmosphere and between the air and the land.
There is no change in angular momentum.
What you have failed to do is accept
1) that you can change the kinetic energy and momentum independently and
2) that you are plainly wrong; nothing can change the angular momentum of an isolated system like the earth and its atmosphere.
If you are not wrong then Noether's theorem is.
Can you point out his mistake please?

[Airthumbs (OP)]

Didn't Feynman touch on that in one of his lectures?

If he did then I was asleep when I listened to it, which begs the question, am I subconsciously learning by listening to all these lectures,documentaries and podcasts during my sleep?  []

[Geezer]

Unless you accept that the earth's atmosphere is part of the earth.

So, either there's no overall effect (provided that you don't think the atmosphere is part of the earth) or there's a temporary effect (which dies out rather rapidly).

Take your pick, but the idea that "It does not need to "keep going". The work was done, and that's all it takes to alter the state of the system." is wrong.

Incidentally cows generally burp more than they fart so the net effect would be the reverse of that predicted.

BC, what you are obviously failing to grasp is that the mass accelerated by the cows is a consequence of work done by chemical processes. Chemical energy was converted into kinetic energy, and added to the kinetic energy of the system as a whole.

Not only have I grasped it, I have understood the consequence of it.I also understood that the kinetic energy is rapidly converted to heat by friction within the atmosphere and between the air and the land.
There is no change in angular momentum.
What you have failed to do is accept
1) that you can change the kinetic energy and momentum independently and
2) that you are plainly wrong; nothing can change the angular momentum of an isolated system like the earth and its atmosphere.
If you are not wrong then Noether's theorem is.
Can you point out his mistake please?

He didn't make a mistake, but you seem to be assuming his theorem requires that there will only be a temporary change

or there's a temporary effect (which dies out rather rapidly).

in the angular velocity of the Earth (that's the chunk of solid stuff you are sitting on which I believe the OP was concerned about). Just because the angular momentum of any arbitrarily defined system is conserved it does not prevent permanent changes in the kinetic energies of the components of that system.

If we were daft enough to change the period of the Earth's rotation with some really powerful rockets, the change in the Earth's period would not die out rather rapidly. Similarly, if cows were able to affect a change in the Earth's period (by converting chemical energy), there is no reason to believe that the change would die out rather rapidly.   

[Bored chemist]

"If we were daft enough to change the period of the Earth's rotation with some really powerful rockets"
Do you accept that we couldn't do that if the rocket exhaust was contained within the earth's atmosphere?
The rockets throw hot gas back, that gas pushes the air and that air pushes the ground so there's no net torque.



"...does not prevent permanent changes in the kinetic energies of the components of that system."
Nope, but friction and viscosity do say exactly that.

I'm not assuming there's a temporary effect.
I'm saying that, for the system as a whole (rock, cows, farts and atmosphere) i.e the earth there is never a change in angular momentum.
For some parts of that system there will be a temporary change but it will die out as the air comes to rest WRT the rock.
Do you think that the cow fart will carry on circling the world forever?
Do you realise that if it stops going round then it hasn't got angular momentum?

Imagine I get a frictionless tube all round the world and I fire a ball bearing round it.
In doing so I transfer angular momentum from the world as a whole to the ball.
From the point of view of an external observer the earth rotates a bit one way, and the ball goes the other.
From our point of view watching the stars, the world changes it's rate of spin (to a tiny extent unless it's a really big fast ball).

OK, now I add some air to the tube. It brings the ball to a halt via viscosity. The ball is slowed down by the air and  by Newton's law it must exert a force on the air. That air, in turn exerts a force on the tube. The tube exerts a force on the earth and so the earth ends up spinning at exactly the same rate as it was before.
We have expended some energy, but all we did was warm the apparatus up a bit. In the long run we didn't alter the speed of the earth's rotation.
The cow farting experiment is much the same.
Nothing leaves the system, so the system conserves momentum

[Geezer]

Sorry for the unusual formatting, but it seemed like a good idea at the time  []

"If we were daft enough to change the period of the Earth's rotation with some really powerful rockets"
Do you accept that we couldn't do that if the rocket exhaust was contained within the earth's atmosphere?
The rockets throw hot gas back, that gas pushes the air and that air pushes the ground so there's no net torque.

I see no reason to accept that. Your argument is based on an unproven assumption that the mass distribution within your system is has not changed.

"...does not prevent permanent changes in the kinetic energies of the components of that system."
Nope, but friction and viscosity do say exactly that.

Again, you seem to be making an assumption about the distribution of mass.

I'm not assuming there's a temporary effect.

Pardon me, but I seem to remember that's exactly what you said.

I'm saying that, for the system as a whole (rock, cows, farts and atmosphere) i.e the earth there is never a change in angular momentum.

I actually agree with you, but that in no way requires that the angular moments of the various components of the system remain constant.

For some parts of that system there will be a temporary change but it will die out as the air comes to rest WRT the rock.
Do you think that the cow fart will carry on circling the world forever?
Do you realise that if it stops going round then it hasn't got angular momentum?

See above. If you can prove that the the distribution of mass within the system remained constant, you might be able to make that case. Does friction play a part? Yes, I'm sure it does, but you have not quantified any time constants associated with that effect other than to say it "dies out".

Imagine I get a frictionless tube all round the world and I fire a ball bearing round it.
In doing so I transfer angular momentum from the world as a whole to the ball.
From the point of view of an external observer the earth rotates a bit one way, and the ball goes the other.
From our point of view watching the stars, the world changes it's rate of spin (to a tiny extent unless it's a really big fast ball).

OK, now I add some air to the tube. It brings the ball to a halt via viscosity. The ball is slowed down by the air and  by Newton's law it must exert a force on the air. That air, in turn exerts a force on the tube. The tube exerts a force on the earth and so the earth ends up spinning at exactly the same rate as it was before.
We have expended some energy, but all we did was warm the apparatus up a bit. In the long run we didn't alter the speed of the earth's rotation.
The cow farting experiment is much the same.
Nothing leaves the system, so the system conserves momentum

Quite right. Yes, I'm not arguing that the system conserves angular momentum. Just because it does, it does not mean that the kinetic energies, or angular velocities, of the components of the system are conserved. Any long term changes in the mass distribution within the system will result in long term changes in the velocities of the components of the system.

Of course, the whole "cow fart" idea is a bit ridiculous, but it does raise an interesting question about what might happen if we really could produce sufficient thrust to alter the period of the Earth's rotation. If I understand BC's argument properly, he is saying that the effect would be rather short lived, and his arguments have a lot of merrit.

I'm coming at it from a different perspective. If we consider the situation of a planet with no atmosphere, I think we could make it rotate faster (or slower). To me, this suggests that an atmosphere will provide a sort of (very complicated) damping function, but ultimately, there will be a change in the angular velocity of the planet in question.

[Bored chemist]

"I see no reason to accept that."

Imagine we put a huge spherical shell round the earth.
Do you accept that we cannot change the total angular momentum of that shell and the earth within it from inside?

That shell is called the atmosphere.

"Again, you seem to be making an assumption about the distribution of mass."
Yes, I am. I am assuming that the moment of inertia doesn't change. I will come back to that.
Suffice it to say that a building will have an effect, but it's small, and it's clearly nothing to do with kinetic energy as you were trying to suggest earlier.


"I'm not assuming there's a temporary effect.

Pardon me, but I seem to remember that's exactly what you said."
Yes, I did say that specifically in response to this.
"He didn't make a mistake, but you seem to be assuming his theorem requires that there will only be a temporary change"
The theory does say that there will be no change. If you only consider the rock, then there will be a temporary change. It seems silly to consider the two independently because, of course, they rotate together. As I said, there isn't a 1000 MPH wind at the equator.


"but it does raise an interesting question about what might happen if we really could produce sufficient thrust to alter the period of the Earth's rotation. "

Of course we could (in principle) do it, in fact, we have. We launched pioneer etc. The effect is small.
In doing so we stopped it being part of the "system" called earth and it gave us something to push against.
The angular momentum of  the system composed of the Earth and Pioneer together, has exactly the same angular momentum as it always did. but since some of that is now with Pioneer, the amount left with us is different.



Now there is another effect to consider here, but it's even smaller than the direct push from the farts.

The cows do indeed, do work in forcing out the gas and that work is converted to thermal energy. It warms up the atmosphere slightly.
The atmosphere will expand (to some unimaginably tiny extent) and so, on average it will be further from the Earth's centre.
That will slightly increase the moment of inertia of the system as a whole. (If you like, the skater has put their arms out again)
That means the whole shooting match will, in fact spin slightly slower.
But, again, there's a catch.
The same would be true whichever direction the cows were facing.
If we make the (reasonable) assumption that the cows will fart anyway, and that they have done so for a long time, the effect will have already happened.
So the overall effect of the cows facing  or farting Eastwards is no different from them farting around as usual.

I grant that I have made no attempt to quantify the time scale over which the effect will die out, but my best guess is that it is roughly the time taken for a disturbance in pressure at the cow's back end to reach the ground. That transfer will happen through the interaction of the gas molecules. They travel at the speed of sound. So the relaxation time for the system is (as well as I can judge it) 3 milliseconds or so.

I'd be interested if anyone has a better estimate.

You also ask if I can show that there's no change in mass distribution.
The mass of, for example, the methane and it's distribution is independent of the direction the cow faces.
Whatever effect it has, it isn't going to change when you line them up Eastwards.

[Geezer]

Yes, well, see, BC, I think we agree on some points here.

The angular momentum within a system is conserved - yes, I'm sure there is no arguing with that.

As you pointed out, spinning skaters can change their angular velocity by redistributing their mass.

(I think we both agree on those points).

Now, when a cow farts, there is also a redistribution of mass (and a very small amount of vectored thrust due to the accelerated mass of exhaust gas), soooo, there is a change in angular velocity, and because there was also a redistribution of mass, the angular velocities of the components of the system are under no obligation to return precisely to their former values.

In other words, while the distribution of mass remains altered, the velocities of the components can remain altered too, even though there is no change in the angular momentum of the system as a whole.

If we bring (non-anchored) spacecraft into the debate, we have a choice. We either define our system to include the spacecraft at all times (in which case angular momentum is conserved), or we allow the mass of the spacecraft to escape from the "system", in which case angular momentum is not conserved.

We have a similar option regarding the cow exhaust. If we define our system as the mass of the Earth excluding its atmosphere, the cows converted parts of Earth into gas and transferred that mass to the atmosphere. So, clearly, the cows altered the Earth's mass, and therefore, the Earth's angular momentum was not conserved.

 

[Bored chemist]

"Now, when a cow farts, there is also a redistribution of mass (and a very small amount of vectored thrust due to the accelerated mass of exhaust gas), soooo, there is a change in angular velocity, and because there was also a redistribution of mass, the angular velocities of the components of the system are under no obligation to return precisely to their former values."

That same redistribution of mass will happen whichever way the cow is facing.
It happened yesterday, and it will happen tomorrow.
The carbon cycle (and it's friends)will ensure that, at whatever rate cow farts add methane to the air at an altitude of roughly a meter, other processes will return it (otherwise the concentration of methane in the air would increase continuously).

The "vectored thrust" you talk of is also a non starter. For a start, all thrust is a vector.
More importantly, unless you think that a cow's fart continues round the world forever, you must accept that it's brought to a halt (wrt the earth) by viscosity. The KE is degraded to heat and any momentum is transferred back to the system.

To whatever extent cow farts affect the spin of the earth, they already have done so.

I agree that, if you don't consider the atmosphere as part of the earth then you can change the angular momentum of either by transferring momentum to the other.
It's just that such a dissection isn't sensible because the two are locked together by friction/ viscous drag.
The earth rotates once a day,and so does the air.
As I have said several times now, there is not a thousand mile per hour wind at the equator.

You cannot sensibly consider the rotation of the atmosphere separately from the rotation of the earth (except for a rather short time).

[Geezer]

It's true that the methane will eventually be removed from the atmosphere, but that's not exactly a rapid process. However, I accept that the whole debate is really silly!

It does prompt a more serious question though. In the past, large amounts of gas have been pumped into the atmosphere by volcanoes. I wonder if those emissions were great enough to alter the moment of inertia of the Earth/atmosphere system and alter its rate of rotation?

[Airthumbs (OP)]

It is silly question Geezer which has had a fantastic amount of scientific input. You raise a very valid point, with regard to events such as volcanoes.  How do the forces of nature effect the rotation of planets.   One example for me, supposedly huge amounts of freshwater have been stored in Dams that have shown to cause a minuscule effect to the rotational speed of the Earth.  So redistribution of mass can effect the rotation of the Earth.  I would then ask if the tides in the oceans cause changes, as huge amounts of water are displaced everyday.  I suppose they would do but as they are cyclic the tides cancel the effect.  Could the sheer mass of water moved even contribute towards events such as Earthquakes even?

I would imagine that Olympus Mons has had some kind of effect on the rotation of Mars....


 [ Invalid Attachment ]

[Bored chemist]

The earth is smoother than a billiard ball.
The effects of mountains are tiny and those of anything else are practically non existent.

Methane in the air lasts about 10 years, but that's not the point. The cows fart constantly and the gas is removed constantly so the overall concentration (and distribution) is constant.

[Airthumbs (OP)]

The earth is smoother than a billiard ball.

And if you were to redistribute the mass on a billiard ball you may also find that this effects its rotational axis.....

[Bored chemist]

The earth is smoother than a billiard ball.

And if you were to redistribute the mass on a billiard ball you may also find that this effects its rotational axis.....

Indeed, for example, if I moved all the mass a metre to the left, then I would move its rotational axis a metre to the left.
However, if it started and d=ended billiard ball shaped, then I wouldn't affect its moment of inertia. (assuming uniform density)

[Airthumbs (OP)]

The earth is smoother than a billiard ball.

And if you were to redistribute the mass on a billiard ball you may also find that this effects its rotational axis.....

Indeed, for example, if I moved all the mass a metre to the left, then I would move its rotational axis a metre to the left.
However, if it started and d=ended billiard ball shaped, then I wouldn't affect its moment of inertia. (assuming uniform density)

Just how big are your billiard balls?  I said redistribute the mass on a billiard ball, I am pretty sure I did not say move it a meter to the left?

[Bored chemist]

Sorry, it was a bit early in the morning. I read it as "the mass of...".
What I should have said was that if I redistribute the mass by rotating it through 180 degrees I might not find that the axis had changed.
The point remains that if it starts and ends billiard ball shaped, then the moment of inertia stays the same.
A better analogy might be that if I stripped the paint off a ball, then put it back, I wouldn't alter the moment of inertia very much.

[JP]

And bear in mind we're talking about gas here, which will tend to redistribute fairly smoothly about the earth, rather than lumping to one side.  So I'd expect the axis of rotation would remain constant.

A bit off topic, but with the big earthquakes recently, it's been found that when the mass of the earth shifts a little in such an earthquake, the rate of rotation of the earth changes because of the change of it's moment of inertia: http://www.csmonitor.com/Science/2011/0314/Japan-earthquake-accelerated-Earth-s-rotation-study-finds 

[Geezer]

For those that care to do the math, the mass of the Earth's atmosphere is about a million times less than the solid/liquid mass, and 90% of the mass of the atmosphere is less than 10 miles above the surface. So, even if all of the atmosphere was to suddenly disappear, it would not affect the angular velocity of the Earth very much, although it would make a measureable difference (assuming there was anyone still around to make the measurement.)