Paul Fuller wrote:
> Several times, as carefully as I could I explained that angular momentum 
> is conserved in a closed system.  That is a general principle that is 
> apparently fundamental to the way the universe works. 

Well, it's not just random. All the "conservation" laws are based on 
"symmetry" laws.  Conservation of energy is based on the premise that 
what you do here will act the same as what you do there. Conservation of 
momentum follows from the idea that an experiment you do now will give 
the same results as an experiment you do later. Conservation of angular 
momentum is based on the premise that an experiment you do facing this 
way will give the same results as an experiment facing that way.

There are similar relationships in the quantum world like conservation 
of spin and so on.

I.e., it's not just that it happens to hold. We know *why* it happens to 
hold, and how to tell when we find a situation where it doesn't hold.

Which I personally find pretty cool to know. :-)

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

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Fredrik Eriksson wrote:
> Yeah, but she will have spent it spinning...

"Only God can make a tree? And what of acorns, then? Are we throwing out 
biology?"  ;-)

You're all nerds.

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

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Paul Fuller <pgf### [at] optusnetcomau> wrote:
> Warp wrote:
> > Warp <war### [at] tagpovrayorg> wrote:
> >>   Besides, we can just forget the cable: Simply shoot the projectile and
> >> that's it. With the correct amount of speed it will stop the object from
> >> rotating. Where did the angular momentum go?
> > 
> >   I thought about this and became to a conclusion. You could have explained
> > it if you knew it instead of just saying "you are wrong" without any
> > explanation.

> Several times, as carefully as I could I explained that angular momentum 
> is conserved in a closed system.

  No, you didn't explain anything. You just stated something. More
specifically, I don't remember you explaining precisely how angular
momentum is preserved in the specific case I quoted above (which is
what I asked about).

  Basically your "explanation" was "the angular momentum is conserved
because angular momentum is always conserved". That's not an explanation
of how angular momentum is conserved in the example above.

> Sorry but you continued to assert that friction could cancel out angular 
> momentum and that a spinning closed system could be brought to rest 
> without any external force.

  You have still failed to explain why friction does not reduce angular
momentum. You have simply stated that it doesn't.

  What I don't understand is how a rotating object can produce heat but
still maintain its full angular momentum. You have not explained this
at all.

> I'll admit to being a poor instructor.  I think you have to admit to 
> being a) wrong and b) pig-headed about it.

  That kind of language is indeed not going to receive too much
approval from me.

  Basically what you have stated is "angular momentum is always preserved
because that's how it works, you are wrong, you are stubborn, you are
silly". That is supposed to convince me about anything?

> I will reply to your other posts to try to clear up some of the wrong 
> assertions that you continue to make in them.  It would be nice if you 
> could reply in one coherent go though rather than in dribs and drabs of 
> silliness.

  That kind of attitude and language is not the best possible to get a
positive attitude from my part.

  I want rational explanations, not "you are wrong because you are wrong"
type of null statements.

-- 
                                                          - Warp

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Paul Fuller <pgf### [at] optusnetcomau> wrote:
> Warp wrote:
> > Warp <war### [at] tagpovrayorg> wrote:
> >>   Besides, we can just forget the cable: Simply shoot the projectile and
> >> that's it. With the correct amount of speed it will stop the object from
> >> rotating. Where did the angular momentum go?
> > 
> >   I thought about this and became to a conclusion. You could have explained
> > it if you knew it instead of just saying "you are wrong" without any
> > explanation.
> So now you're saying that *I* don't understand the topic.  Very, very rich.

  OMG. You are deliberately making this into a flamewar.

  Ok, I'll stop, because I'm too prone to get flamed.

  You can think whatever you want.

-- 
                                                          - Warp

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Warp wrote:
>   What I don't understand is how a rotating object can produce heat but
> still maintain its full angular momentum. You have not explained this
> at all.

Angular momentum consists of both velocity and distance. When the skater 
pulls her arms in and speeds up, the muscular energy turns into kinetic 
energy, but the angular momentum stays the same. When the spinning disk 
rubs against the disk spinning the other way, the kinetic energy of the 
disks is turned into the kinetic energy of the individual atoms (i.e., 
heat), but the positive-signed spinning of the top disk cancels the 
negative-signed spinning of the bottom disk.

So, you can change energy without changing angular momentum by spinning 
faster but closer, or by having two things spinning opposite directions 
change their rate of spin the same amount in different directions.

Energy, on the other hand, isn't signed (except in some rather bizarre 
circumstances, and to make the math come out for potential energy in 
situations that never actually occur in reality), so that's how it can 
happen that you can change the form of energy without changing the 
amount of angular momentum.

-- 
   Darren New / San Diego, CA, USA (PST)
     Remember the good old days, when we
     used to complain about cryptography
     being export-restricted?

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Darren New wrote:
> Paul Fuller wrote:
>> Several times, as carefully as I could I explained that angular 
>> momentum is conserved in a closed system.  That is a general principle 
>> that is apparently fundamental to the way the universe works. 
> 
> Well, it's not just random. All the "conservation" laws are based on 
> "symmetry" laws.  Conservation of energy is based on the premise that 
> what you do here will act the same as what you do there. Conservation of 
> momentum follows from the idea that an experiment you do now will give 
> the same results as an experiment you do later. Conservation of angular 
> momentum is based on the premise that an experiment you do facing this 
> way will give the same results as an experiment facing that way.
> 
> There are similar relationships in the quantum world like conservation 
> of spin and so on.
> 
> I.e., it's not just that it happens to hold. We know *why* it happens to 
> hold, and how to tell when we find a situation where it doesn't hold.
> 
> Which I personally find pretty cool to know. :-)
> 
I don't think I implied that it is random.  If so then let me clear that up.

What I said was 'apparently fundamental to the way the universe works'. 
    Just my choice over declaring it a 'law'.  Certainly not random or 
by accident.

We can understand that "you can't create something out of nothing" or 
"everything must be balanced".  Statements of principles that help us to 
investigate and understand everything else.

I don't think you can explain though why those principles are true 
without essentially coming back to restating them or observing that 
we've never seen them to be broken.  So I'll call them fundamental. 
They are the rules of the game.  The pieces follow the rules not because 
they want to but because there simply is no way not to.

Sure they match our sense of fair play.  Perhaps even our sense of fair 
play is based on the fundamental principle rather than the other way 
around ?

When you say the "Conservation of energy is based on the premise ..." 
and "Conservation of momentum follows from the idea ...", I would 
instead say that the premise and the idea are based on the fundamental 
principles.

And it is cool :)

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Darren New <dne### [at] sanrrcom> wrote:
> Angular momentum consists of both velocity and distance. When the skater 
> pulls her arms in and speeds up, the muscular energy turns into kinetic 
> energy, but the angular momentum stays the same. When the spinning disk 
> rubs against the disk spinning the other way, the kinetic energy of the 
> disks is turned into the kinetic energy of the individual atoms (i.e., 
> heat), but the positive-signed spinning of the top disk cancels the 
> negative-signed spinning of the bottom disk.

  If we express that in overly simple terms: If a rotating system consists
of several parts, bringing those parts closer together requires energy.
If those parts are later pulled apart, that energy is released?

  Or perhaps in another way: Bringing more variation to local spinning
at different parts of the system requires energy, but evening out the
local variations and bringing the whole system to a more even state
(with less local variations in spin) releases that energy?
  (In other words, in a closed system getting two discs to rotate
independently in the same direction requires energy. Colliding those
discs so that they will start rotating as one single object will release
that energy?)

-- 
                                                          - Warp

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You've selectively quoted the bits where I have been peeved with your 
lack of comprehension after several attempts.  All the bits where I have 
tried to explain to you the underlying physics seem to have passed right 
by you.

So I'll forget everything else and just try to explain the heart of it.

You misunderstand what angular momentum is.  Stop thinking that the 
angular momentum of a system is just the one part that is obviously 
spinning around.

The angular momentum of a system is the sum of the mass * velocity * 
radius of every single part of the system all taken relative to some 
reference point.

Mass and velocity should be clear.

Radius is the perpendicular distance from the reference point to the 
velocity vector.  Thus if the velocity vector passes exactly through the 
reference point the contribution to angular momentum is zero.  Any 
particle in the system that is moving and the velocity vector does not 
point exactly through the reference point contributes angular momentum 
to the total.  Now the contribution can be positive or negative 
depending on the sign of the velocity and which side of the reference 
point it falls on.

You can choose any reference point so long as it remains fixed.  It is 
often convenient to take the centre of mass of the system as the 
reference point when considering angular momentum.  Note that the centre 
of mass of a closed system is fixed within the frame of reference of 
that system.

Consider a closed system consisting of mass A that is not spinning and 
object B that is spinning.  Suppose A is the fixed frame of a satellite 
and B is the spinning wheel of a gyroscope.  All of the angular momentum 
of the system is contributed by the spinning mass B for now.  Let the 
total angular momentum be K.  K is currently not zero and lets say we 
choose our units and reference point etc so that it comes out as +100 
units.  The SI unit for angular momentum is Newton metre seconds (Nms) 
or Kgm^2s^-1.

Note that B possesses both angular momentum and kinetic energy.

Now apply a brake between A and B that brings them completely to rest 
with respect to each other.  The kinetic energy is converted heat.  As 
far as this closed system is considered there is no more usable kinetic 
energy available it has all been converted to heat.

Where is the angular momentum?  Well in applying a braking force to B, 
object A has experienced an equal and opposite force.  This causes it to 
start spinning.  In fact the whole system is now spinning compared to an 
external reference system.

The spin is in the same direction as the object B was spinning.  But A+B 
is not spinning at the same rate as B was alone.

How fast is it spinning and what is the new total angular momentum? 
Well it is spinning exactly fast enough so that calculating the mass * 
velocity * radius of every particle and adding them up comes to K as 
before.  Exactly.  There is no conversion of angular momentum to or from 
any form of energy.

Saying that K remains the same is not saying that there is any usable 
kinetic energy left in the system.  So forget the idea of perpetual motion.

The system had net angular momentum of K at the start, the end and at 
every intermediate point.

Considering it the opposite way around, if a satellite is spinning it 
can start to spin some part of itself in the opposite direction.  If 
this is done precisely enough then the satellite stops spinning but only 
so long as it keeps the gyroscope spinning at that speed and direction. 
  As friction slows down the gyroscope the satellite will start to spin 
again.  It can keep pumping in energy to maintain the rate of spin to 
keep itself pointed in one direction.  So energy keeps having to be 
introduced and it comes back out as heat due to friction.  This does not 
at any time alter the total angular momentum of the system.  AM has been 
transferred to the gyroscope and is stored there to come back out later.

If on the other hand thrusters are used to halt the rotation then the 
expelled particles carry away the angular momentum.  They are masses 
moving with velocity at a perpendicular distance to the reference point. 
    The particles in the thruster stream themselves don't need to be 
spinning to carry angular momentum relative to the reference point by 
the way.

Angular momentum is something different to energy and has its own 
accounting ledger.  The ledger always has to balance and you can't 
transfer amounts from the angular momentum ledger to or from the energy 
ledger.  Same with linear momentum.  It has its own ledger that always 
balances and likewise you can't transfer into or out of it from either 
energy or angular momentum.

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Paul Fuller <pgf### [at] optusnetcomau> wrote:
> If on the other hand thrusters are used to halt the rotation then the 
> expelled particles carry away the angular momentum.

  A theoretical question: Can mass be converted to other forms of energy?
(I think GR said something about this?)

  Assuming yes, how does this conversion affect angular momentum?

-- 
                                                          - Warp

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Warp wrote:
> Paul Fuller <pgf### [at] optusnetcomau> wrote:
>> If on the other hand thrusters are used to halt the rotation then the 
>> expelled particles carry away the angular momentum.
> 
>   A theoretical question: Can mass be converted to other forms of energy?
> (I think GR said something about this?)
Yes.
> 
>   Assuming yes, how does this conversion affect angular momentum?
> 
Simple - a photon carries angular momentum.

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