# The Naked Scientists Forum

### Author Topic: Can cow farts make the Earth rotate faster?  (Read 57023 times)

#### Geezer

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##### Can cow farts make the Earth rotate faster?
« Reply #25 on: 05/07/2011 17:34:30 »
BC - Angular momentum only applies to a rigid body.

It's simply a case of F=ma. The accelerated mass of methane results in a force that applies a torque, communicated through the cow's hooves, to the Earth.

If angular momentum was conserved, jet engines (or rockets for that matter) would not work.

#### JP

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##### Can cow farts make the Earth rotate faster?
« Reply #26 on: 05/07/2011 18:21:49 »

Newtons laws show that there would be no net effect.

BC, think about that the next time you are in an aeroplane, because, if you are right, it ain't going anywhere.
A lot of people might have correctly assumed that I meant no effect on the Earth's rotation.

Obviously there would be effects. For example, if you were behind the cows you would probably notice. If you were smoking at the time you might notice something else too.
However neither the flatulent cows, not my air travel make much odds to the Earth's rotation.

If the cows were all pointing their bums in the same direction, the net effect would be nonzero. Admittedly it would be very difficult to detect the effect, but Newton's laws would still apply.

Still wrong.
http://en.wikipedia.org/wiki/Angular_momentum

I'm not sure how angular momentum disproves the effect.  If anything, it shows why there has to be an effect.  It's a simplification, but basically the cows will cause the atmosphere to pick up a tiny bit of circulation in the direction of their derrieres.  The atmosphere therefore gains some angular momentum.  Since the earth is basically a closed system, it's total angular momentum can't change, so the earth's rotation would have to change slightly to make up for the atmosphere.

The real effect would be minuscule, however.

Geezer's post is another way of looking at it, where the earth is your system and the cow "rockets" are an external torque.

#### Geezer

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##### Can cow farts make the Earth rotate faster?
« Reply #27 on: 05/07/2011 18:34:17 »

Newtons laws show that there would be no net effect.

BC, think about that the next time you are in an aeroplane, because, if you are right, it ain't going anywhere.
A lot of people might have correctly assumed that I meant no effect on the Earth's rotation.

Obviously there would be effects. For example, if you were behind the cows you would probably notice. If you were smoking at the time you might notice something else too.
However neither the flatulent cows, not my air travel make much odds to the Earth's rotation.

If the cows were all pointing their bums in the same direction, the net effect would be nonzero. Admittedly it would be very difficult to detect the effect, but Newton's laws would still apply.

Still wrong.
http://en.wikipedia.org/wiki/Angular_momentum

I'm not sure how angular momentum disproves the effect.  If anything, it shows why there has to be an effect.  It's a simplification, but basically the cows will cause the atmosphere to pick up a tiny bit of circulation in the direction of their derrieres.  The atmosphere therefore gains some angular momentum.  Since the earth is basically a closed system, it's total angular momentum can't change, so the earth's rotation would have to change slightly to make up for the atmosphere.

The real effect would be minuscule, however.

Geezer's post is another way of looking at it, where the earth is your system and the cow "rockets" are an external torque.

So, basically you are saying the atmospheric effect is a BUM STEER?
« Last Edit: 05/07/2011 18:38:24 by Geezer »

#### Airthumbs

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##### Can cow farts make the Earth rotate faster?
« Reply #28 on: 05/07/2011 18:40:38 »
Geezer's post is another way of looking at it, where the earth is your system and the cow "rockets" are an external torque.

#### Bored chemist

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##### Can cow farts make the Earth rotate faster?
« Reply #29 on: 05/07/2011 19:08:25 »
The cows' farts would push the air and the air would push the ground. After a very short while the effect would cancel out.

Because of the friction between the earth and its atmosphere, you cannot treat the two as separate systems (for long).
Since (in anything but the very short term) there's only one system, it has conserved angular momentum and its rate of rotation is conserved too.

Also, if as Geezer thinks, angular momentum is only conserved for rigid bodies, why is the classic example in all the textbooks a spinning skater who pulls there arms in and speeds up. If they pull their arms in they cannot be rigid.
It's clear that the cows' hooves push the ground, but as I pointed out earlier, so do the farts and the two effects cancel.
They have to cancel exactly because the earth, the fart, the cow, and the atmosphere are all part of one system and the momentum of that system cannot be altered by anything internal to the system.
If the cows farted into orbit then there would be an effect.
« Last Edit: 05/07/2011 19:19:50 by Bored chemist »

#### JP

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##### Can cow farts make the Earth rotate faster?
« Reply #30 on: 05/07/2011 20:13:16 »
They have to cancel exactly because the earth, the fart, the cow, and the atmosphere are all part of one system and the momentum of that system cannot be altered by anything internal to the system.
If the cows farted into orbit then there would be an effect.

They're all the same system so the total angular momentum can't change.  But parts of the system can change, which is why if the angular momentum of the atmosphere decreases, that of the earth increases.  This is exactly the effect caused by the cows.

#### Geezer

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##### Can cow farts make the Earth rotate faster?
« Reply #31 on: 05/07/2011 21:06:05 »
Also, if as Geezer thinks, angular momentum is only conserved for rigid bodies, why is the classic example in all the textbooks a spinning skater who pulls there arms in and speeds up.

In that situation you either treat the skater as different rigid bodies at different points in time or, as a very large number of rigid bodies, each of which has its own angular momentum, and integrate their effects at any point in time.

Oh, and the angular velocity of the skater only changed because work was done within the system of the skater.

#### Bored chemist

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##### Can cow farts make the Earth rotate faster?
« Reply #32 on: 05/07/2011 21:09:52 »
I don't think it makes sense to say that the atmosphere and the rock can be treated as separate systems when, as I have pointed out before, they are linked.
Have you noticed the thousand mile an hour wind at the equator?
No, that's because it isn't there. The atmosphere rotates along with the planet and that's because it's part of the planet.
As I have pointed out, there would be a temporary change but its wouldn't last.

If the cows walked East, then they would push the earth West, and, for as long as they kept walking, they would change the spin of the earth. But the thing is that when they stop they exert a force on the Earth and in doing so they push it East a bit and the Earth's spin goes back to what it was.
In the case of the "grand fart" the angular momentum transfer cannot be sustained because the farts don't keep going.

The bit about the skater doing work isn't relevant. You can change the angular velocity without doing net work. It would be odd, but it's perfectly possible.
I will now look forward to your description of the orbiting earth and the sun, with a vast gap between them somehow being a rigid system in order that angular momentum is conserved.
When you have done that perhaps you could explain how tidal drag- which kind of requires a non rigid system  (usually something sloshy) is explained in terms of the conservation of angular momentum.

Any isolated system conserves angular momentum. It does not need to be rigid. This is just as well, since no object is truly rigid anyway.
« Last Edit: 05/07/2011 21:15:44 by Bored chemist »

#### Geezer

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##### Can cow farts make the Earth rotate faster?
« Reply #33 on: 05/07/2011 21:16:21 »
In the case of the "grand fart" the angular momentum transfer cannot be sustained because the farts don't keep going.

It does not need to "keep going". The work was done, and that's all it takes to alter the state of the system.

Take the atmosphere out of it and consider what would happen if you attached a very large rocket to the moon. It would obviously cause the moon's angular velocity to increase as long as the rocket was firing. Once it stopped firing, the moon would continue rotating with a new angular velocity.

#### Bored chemist

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##### Can cow farts make the Earth rotate faster?
« Reply #34 on: 05/07/2011 21:25:49 »
You keep muddling up energy and momentum.

Also you missed a bit from your model

"It would obviously cause the moon's angular velocity to increase as long as the rocket was firing suff into space "

The combined angular momentum of the exhaust going clockwise is exactly the same as the anticlockwise change in the angular momentum of the moon.
The change of angular momentum of the system is still zero, and it will always be so. That's the point about conservation laws.
It's not just an approximation for rigid systems, it isn't just a figment of my imagination. It's a mathematical law, provable from first principles.
http://en.wikipedia.org/wiki/Noether%27s_theorem
It's true now, and it will still be true in the morning.

#### JP

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##### Can cow farts make the Earth rotate faster?
« Reply #35 on: 05/07/2011 21:49:49 »
Are we talking about permanent increase in rotation or temporary increase.

It's true that immediately after the cows all fire, and before friction does too much, the earth will respond by speeding up, at least temporarily.

#### Bored chemist

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##### Can cow farts make the Earth rotate faster?
« Reply #36 on: 05/07/2011 21:57:43 »
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.

#### Geezer

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##### Can cow farts make the Earth rotate faster?
« Reply #37 on: 05/07/2011 22:07:01 »
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.

« Last Edit: 05/07/2011 22:41:14 by Geezer »

#### Airthumbs

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##### Can cow farts make the Earth rotate faster?
« Reply #38 on: 05/07/2011 23:28:35 »
I honestly did not think that what appeared to be such a simple question was in fact quite complicated indeed!

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

#### Geezer

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##### Can cow farts make the Earth rotate faster?
« Reply #39 on: 06/07/2011 00:18:16 »
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

#### Airthumbs

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##### Can cow farts make the Earth rotate faster?
« Reply #40 on: 06/07/2011 00:28:02 »
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

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##### Can cow farts make the Earth rotate faster?
« Reply #41 on: 06/07/2011 04:28:16 »
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

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##### Can cow farts make the Earth rotate faster?
« Reply #42 on: 06/07/2011 05:18:37 »
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

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##### Can cow farts make the Earth rotate faster?
« Reply #43 on: 06/07/2011 06:56:19 »
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?
« Last Edit: 06/07/2011 07:00:46 by Bored chemist »

#### Airthumbs

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##### Can cow farts make the Earth rotate faster?
« Reply #44 on: 06/07/2011 14:51:07 »
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

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##### Can cow farts make the Earth rotate faster?
« Reply #45 on: 06/07/2011 17:54:28 »
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

Quote
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

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##### Can cow farts make the Earth rotate faster?
« Reply #46 on: 06/07/2011 20:13:49 »

"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
« Last Edit: 06/07/2011 20:42:38 by Bored chemist »

#### Geezer

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##### Can cow farts make the Earth rotate faster?
« Reply #47 on: 08/07/2011 11:01:45 »
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.
« Last Edit: 08/07/2011 11:07:34 by Geezer »

#### Bored chemist

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##### Can cow farts make the Earth rotate faster?
« Reply #48 on: 08/07/2011 18:58:43 »
"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

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##### Can cow farts make the Earth rotate faster?
« Reply #49 on: 12/07/2011 06:21:20 »
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.

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##### Can cow farts make the Earth rotate faster?
« Reply #49 on: 12/07/2011 06:21:20 »