[Bored chemist]

It is easy to show that adding energy to a rigid body can change the axis of rotation,

Then show it.
But no cheating.
You have to do it without applying a torque.
Only add energy.

[Jaaanosik]

Yes, the axis will be there but the angular velocity around this axis will be changing during the flip/transition.

Yes it will

And so will the moment of inertia; it will also change; in lock step with the rotation rate.

But the product or the two, which is the angular momentum,  will be constant.
The angular momentum is a conserved quantity. The angular velocity and the moment of inertia are not conserved.

Which is what the science has said all along.

How do boundary conditions work?
Let us say the ice can transition/flip lasts 10s.
The ant lives 50 microseconds sometimes during the flip.
The ant will observer big changes not knowing where they come from.
The changes in the 50 microseconds span are dependent on the boundary conditions.
Where and when the ant lives.

Going to the OP. The same applies.
We are ants and the windmill is a tiny factor in all the big changes and it can under the right conditions influence the Earth acceleration.
That was the question, about the rotation and specifically acceleration.
There could be an angular velocity change (an angular acceleration) even though 'the total big angular momentum would be conserved'.

[Bored chemist]

How do boundary conditions work?

You draw a boundary round the relevant thing- in this case the tin, its contents and the ant. And say that's the system under consideration

And then you measure the total angular momentum of the system
And you find it is constant.

It is easy to show that adding energy to a rigid body can change the axis of rotation,

Then show it.
But no cheating.
You have to do it without applying a torque.
Only add energy.

[Jaaanosik]

How do boundary conditions work?

You draw a boundary round the relevant thing- in this case the tin, its contents and the ant. And say that's the system under consideration

And then you measure the total angular momentum of the system
And you find it is constant.

It is easy to show that adding energy to a rigid body can change the axis of rotation,

Then show it.
But no cheating.
You have to do it without applying a torque.
Only add energy.

You cannot measure it with high enough precession therefore it is not going to be constant.

[gem]

Hi all,

So BC

You can't make energy into angular momentum.
If you could it would break both conservation laws.

I agree,
however thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation.

Given the gas laws and momentum of a particle and subsequent pressure are temperature dependent,(PV=nRT)
as radiation is emitted to space temperature decreases as does momentum.

Now given the atmosphere does not fulfil the criteria for conservation of energy or momentum.

there appears to be a contradiction in this statement

Yes, I agree.
But the point remains. The atmosphere may "borrow" angular momentum from the solid Earth (Though, even for a hurricane, the effect is tiny) but, the sum of their momenta is still the same as it was. And when the hurricane stops, it returns exactly the same angular momentum as it "borrowed.
For the planet earth, as a whole, including the atmosphere, the angular momentum is constant.

Now BC this is not a criticism it is one of the contradictions I referred to when i joined this thread.

So if you consider option 3 you get the same effect for opposite reasons.


"If you follow the logic that the atmosphere is changing momentum continually (therefore not conserved)  and is able to transfer exchange momentum with the earth's surface via collision/friction, which is observed in the data of LOD, we have several options to consider.

1, No change in momentum has occurred

2, The forces of the trade winds and polar winds 0-30 and 60-90 degree regions, are exactly matched by the prevailing winds in the 30-60 degree regions so LOD is maintained.

3, , The forces of the trade winds and polar winds 0-30 and 60-90 degree regions, that have frictional contact with the surface, are NOT exactly matched by the prevailing winds in the 30-60 degree regions, would require a external torque force. (ie the LOD is the earth's terminal velocity, balance between all frictional drag and external force)

and I edit your statement to read;

 Yes, I agree.
But the point remains. The atmosphere transfers to and borrows angular momentum from the solid Earth (Though, even for a hurricane, the effect is tiny) but, the sum of their momenta is still the same as it was. when the hurricane stops, it returns to exactly the same angular momentum.
For the planet earth, as a whole, including the atmosphere, the angular momentum is constant.

[Bored chemist]

How do boundary conditions work?

You draw a boundary round the relevant thing- in this case the tin, its contents and the ant. And say that's the system under consideration

And then you measure the total angular momentum of the system
And you find it is constant.

It is easy to show that adding energy to a rigid body can change the axis of rotation,

Then show it.
But no cheating.
You have to do it without applying a torque.
Only add energy.

You cannot measure it with high enough precession therefore it is not going to be constant.

Actually, in context, I can.
I can point out that Stonehenge is still lined up with the solstice.

You seem to be forgetting to address this issue:

Quote from: Bored chemist on Yesterday at 00:33:01
Quote from: Bored chemist on 24/09/2020 19:01:18
Quote from: Jaaanosik on 24/09/2020 18:51:25
It is easy to show that adding energy to a rigid body can change the axis of rotation,
Then show it.
But no cheating.
You have to do it without applying a torque.
Only add energy.

[Bored chemist]

Now given the atmosphere does not fulfil the criteria for conservation of energy or momentum.

Whoa there.
That particular logical fallacy is called "begging the question"; don't do it again.
Who says it doesn't.
Again you seem to be linking momentum with energy.
The atmosphere picks up energy from the Sun.
But it can't pick up angular momentum from anything but the planet Earth.
And it will, in the long run, always return that so, overall, it has conserved  angular momentum.

there appears to be a contradiction in this statement

No, there isn't.
You just think there is because you do not accept that momentum and energy are separate.

What I said was"But the point remains. The atmosphere may "borrow" angular momentum from the solid Earth (Though, even for a hurricane, the effect is tiny) but, the sum of their momenta is still the same as it was. And when the hurricane stops, it returns exactly the same angular momentum as it "borrowed.
For the planet earth, as a whole, including the atmosphere, the angular momentum is constant."


For the planet earth, as a whole, including the atmosphere, the angular momentum is constant.
If you edit it and still say it's my statement then you are lying.

If you need to lie to prove your "point" then you have accepted that you can't do it honestly.
If you can't honestly prove your point, you know your point isn't true.

You seem not to accept that the atmosphere is part of the Earth and that the Earth as a whole must, at all times,  have a constant angular momentum.

[gem]

So BC not sure where the misunderstanding came from for this

If you edit it and still say it's my statement then you are lying.

Your statement;

  Yes, I agree.
But the point remains. The atmosphere may "borrow" angular momentum from the solid Earth (Though, even for a hurricane, the effect is tiny) but, the sum of their momenta is still the same as it was. And when the hurricane stops, it returns exactly the same angular momentum as it "borrowed.
For the planet earth, as a whole, including the atmosphere, the angular momentum is constant.

So to repeat the point, and to make clear this is coming to very similar results for very different reasons as stated in the previous post. 

If you consider option 3 you get the same effect for opposite reasons.

1, No change in momentum has occurred

2, The forces of the trade winds and polar winds 0-30 and 60-90 degree regions, are exactly matched by the prevailing winds in the 30-60 degree regions so LOD is maintained.

3, , The forces of the trade winds and polar winds 0-30 and 60-90 degree regions, that have frictional contact with the surface, are NOT exactly matched by the prevailing winds in the 30-60 degree regions, would require a external torque force. (ie the LOD is the earth's terminal velocity, balance between all frictional drag and external force)

It would be reasonable to expect  the atmosphere transfers to and borrows angular momentum from the solid Earth (Though, even for a hurricane, or extreme winds especially near mountain ranges with a east or west net force the effect is tiny but measurable) but, the sum of their momenta returns to approximately the same as it was. when the hurricane/extreme weather stops, it returns to approximately the same angular momentum.
For the planet earth, as a whole, including the atmosphere.

Now given you now state quite correctly that the atmosphere transfers momentum to the solid earth and the solid earth transfers momentum back, and this is stated to be done by frictional coupling, brings us back to heat and to my statement from the last post

 
however thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation.

Given the gas laws and momentum of a particle and subsequent pressure are temperature dependent,(PV=nRT)
as radiation is emitted to space temperature decreases as does momentum.

So How does your statement;

  And when the hurricane stops, it returns exactly the same angular momentum as it "borrowed.

 Allow for this loss of momentum due to the continual exchange of momentum between the earth's surface and the atmosphere due to the conversion of kinetic momentum to heat momentum due to frictional coupling and subsequent radiation and temperature decrease resulting in decrease in the thermal motion of particles. (PV=nRT)
Therefore a reduction in the momentum available to return to whence it was borrowed.

[Bored chemist]

You really need to get to grips with the fact that you can  not convert a scalar quantity like energy into a vector quantity like angular momentum.

You have forgotten that what started the hurricane spinning in the first place is that it was pushed by the earth- that's why they spin in opposite directions either side of the equator.

So, as the winds die down and are slowed by friction with the Earth's surface, they return the same angular momentum they borrowed earlier; neither more not less.

but, the sum of their momenta returns to approximately the same as it was

No; it's exactly the same angular momentum.
Do you not accept that angular (and linear) momentum is conserved during  every single collision between molecules in the air?

And since it is conserved in all those huge numbers of collisions, it is also conserved for the sum of all of them?
Or are you saying that arithmetic does not work?
Are you saying that you can not add things up to get a sum of the individual things?

[gem]

HI all,
So BC

what started the hurricane spinning in the first place is that it was pushed by the earth- that's why they spin in opposite directions either side of the equator.

yes quite agree we covered the coriolis effect previously

https://en.wikipedia.org/wiki/Coriolis_force
 
However on this point;

So, as the winds die down and are slowed by friction with the Earth's surface, they return the same angular momentum they borrowed earlier; neither more not less.

So if there is friction, for both linear and angular momentum means the collision is not perfectly elastic, and therefore a percentage of momentum is transferred to the thermal motion of particles, whether within the earth's surface or the gas particles of the atmosphere.

So if calculated at that instance of transfer, it would be calculated momentum is conserved, overall but the linear/angular
momentum will have altered.

Indeed it would not be possible to determine any difference from this thermal aspect of momentum due to frictional coupling and the thermal momentum occuring because of solar radiation. 

We have discussed at length the process that occur due to the conditions of earth's atmosphere having a pressure gradient and energy input, momentum is constantly changing, and that thermal momentum can be reduced via radiation
to space. (due to reduction in temperature and gas laws PV=nRT )

which means this statement

No; it's exactly the same angular momentum.

cannot be correct.

Given friction occurs, momentum is transferred in both processes of borrowing/returning when frictional coupling with the earth's surface occurs, means a percentage of momentum of the earth is continuously being transferred to thermal motion of particles.

[Bored chemist]

We have discussed at length the process that occur due to the conditions of earth's atmosphere having a pressure gradient and energy input, momentum is constantly changing, and that thermal momentum can be reduced via radiation
to space. (due to reduction in temperature and gas laws PV=nRT )

Yes
And you have ignored a simple fact.

Do you not accept that angular (and linear) momentum is conserved during  every single collision between molecules in the air?

And since it is conserved in all those huge numbers of collisions, it is also conserved for the sum of all of them?
Or are you saying that arithmetic does not work?
Are you saying that you can not add things up to get a sum of the individual things?

Friction "degrades" kinetic energy to heat.
But it doesn't destroy momentum; it just transfers it.

means a percentage of momentum of the earth is continuously being transferred to thermal motion of particles.

And vice versa.

You still don't seem to have got to grips with the fact that momentum is a conserved quantity unless there's an external torque.
You also don't seem to have grasped the fact that momentum and energy are different.
At least Jaaanosik has recognised that he was wrong to say this, and gone away.

Quote from: Jaaanosik on 26/09/2020 23:27:18
Quote from: Bored chemist on Yesterday at 00:33:01
Quote from: Bored chemist on 24/09/2020 19:01:18
Quote from: Jaaanosik on 24/09/2020 18:51:25
It is easy to show that adding energy to a rigid body can change the axis of rotation,
Then show it.
But no cheating.
You have to do it without applying a torque.
Only add energy.

[gem]

Hi all,
So BC when I stated

  So if there is friction, for both linear and angular momentum means the collision is not perfectly elastic, and therefore a percentage of momentum is transferred to the thermal motion of particles,

your response;

And vice versa.

now given I stated this in the same post;

Indeed it would not be possible to determine any difference from this thermal aspect of momentum due to frictional coupling and the thermal momentum occuring because of solar radiation.

what is the mechanism that discriminates/separates the thermal motion of particles generated by,

1. frictional coupling
2. solar radiation

to allow this statement to be correct;
 

No; it's exactly the same angular momentum.

[Bored chemist]

  So if there is friction, for both linear and angular momentum means the collision is not perfectly elastic, and therefore a percentage of momentum is transferred to the thermal motion of particles,

And vice versa.

So
So if there is no friction, for both linear and angular momentum means the collision is not perfectly elastic, and therefore a percentage of
 no momentum is transferred to the thermal motion of particles,

You can't turn a scalar quantity into a vector one.
You can't make  energy into momentum.
If I wrote something that said otherwise then I was mistaken. Opps!, Sorry about that.
But the fact remains that the quantities are all independently conserved.

[Bored chemist]

what is the mechanism that discriminates/separates the thermal motion of particles generated by,

Symmetry.

[gem]

Hi all.
So in regards to; if there is no friction, for both linear and angular momentum means the collision is perfectly elastic, and therefore
no momentum is transferred to the thermal motion of particles.
Yes think we can all agree on that.

However you seem to be backing away from your statement below, which quite correctly highlights there is frictional coupling between the earth's surface and the atmosphere;

So, as the winds die down and are slowed by friction with the Earth's surface, they return the same angular momentum they borrowed earlier; neither more not less.

are you now saying there is no friction between the atmosphere and the earth's surface and therefore no transfer of momentum  to the thermal motion of particles ?

[Bored chemist]

Friction refers to the conversion of mechanical energy to heat energy.
It is not magic.
It still obeys the conservation of angular and linear momentum.

You can not convert energy into momentum.

At the level of individual molecules of gas hitting eachother there is no friction- energy and momenta are conserved.

This is also true for gas molecules hitting the solid earth or the sea surface.

Since energy and momentum are conserved in absolutely every one of these tiny collisions. it follows that energy and momentum must be (exactly) conserved over all.

Why do you not see that you are trying to claim that addition does not work?

[gem]

HI all,
 BC, yes agreed

You can not convert energy into momentum.

I believe we already covered this.
However it is possible to increase/change momentum of the atmosphere due to the conditions/dynamics occurring ie solar input to a fluid changing density in a gravity field creating buoyancy force and subsequent acceleration.

Below is a quote with the link given;
https://en.wikipedia.org/wiki/Momentum

If the forces are not balanced, the droplet accelerates. This acceleration is not simply the partial derivative
∂v
/
∂t
 because the fluid in a given volume changes with time.

Applied to any physical quantity, the material derivative includes the rate of change at a point and the changes due to advection as fluid is carried past the point. Per unit volume, the rate of change in momentum is equal to
ρ Dv/Dt  (ρ density)

This is equal to the net force on the droplet.

Forces that can change the momentum of a droplet include the gradient of the pressure and gravity, as above.

Now given the above states quite clearly the atmosphere is capable of changing momentum, and one such cause is change in density due to the solar input constantly changing the balance of the forces,

Therefore  addition doesn't doesnt work if the numbers keep changing.
 

Why do you not see that you are trying to claim that addition does not work?

Now this statement ;

At the level of individual molecules of gas hitting eachother there is no friction- energy and momenta are conserved.

This is also true for gas molecules hitting the solid earth or the sea surface.

Since energy and momentum are conserved in absolutely every one of these tiny collisions. it follows that energy and momentum must be (exactly) conserved over all.

In regards to "At the level of individual molecules of gas hitting each other there is no friction- energy and momenta are conserved"
yes agreed, but I would have stated At the level of individual molecules of gas hitting each other they are elastic collisions

In regards to this part;

 "This is also true for gas molecules hitting the solid earth or the sea surface."

agreed that energy and momentum conserved overall, but given the collision with the surface is not 100% elastic
some kinetic energy is transformed to heat/thermal energy and sound waves and similarly some momentum is transferred to the thermal motion of particles and also momentum carried away in the sound waves emanating out in all directions as per the inverse square law.

when considering the exchange that occurs with the atmosphere and the sea similarly you get heat and thermal motion of particles and also momentum carried by the waves.

Therefore not a 100% exchange rate of the solid earth's or atmospheres, rotational kinetic or angular momentum.

And as covered previously if some momentum is transferred to thermal motion this is now in the same category as the thermal motion due to solar input and open to the same dynamics going forward in time.   

[Bored chemist]

Therefore  addition doesn't doesnt work if the numbers keep changing.

The numbers only change when "something happens" and momentum is conserved during every "something".

So it is conserved overall.

If I explained to the man on the truck that his hands were pushing the truck forward but his feet were pushing it back just as hard, he would probably accept that.
You, on the overhand would say that because he's working really hard - burning lots of calories + sweating, he must be achieving something.

Sometimes, even in physics, it's not the energy you need to look at.

[Bored chemist]

but given the collision with the surface is not 100% elastic
some kinetic energy is transformed to heat/thermal energy

Momentum is conserved during inelastic collisions.
That's how we can still do maths with them.

[Jaaanosik]

Actually, in context, I can.
...
At least Jaaanosik has recognised that he was wrong to say this, and gone away.
...

Keep dreaming , it is about the boundary conditions.
We cannot have right/wrong if were are not talking about the same observers and boundary conditions.