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.

Post a reply to this message

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.

Post a reply to this message

Paul Fuller wrote:
> I don't think I implied that it is random.  If so then let me clear that 
> up.

Sorry. Random is a bad word to use.

That things work the same no matter which way you face is the "random" 
part. It's not necessary that things work that way. But it seems they 
do. *Given* that, conservation of angular momentum is a result.

> 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.  

Right. What I was trying to express is that "angular momentum is 
conserved" isn't really the "we've never seen it to be broken" part. 
It's the "experiments run the same no matter which way you face" that's 
the "never seen to be broken part".  Conservation of angular momentum is 
an effect, not a cause.

> And it is cool :)

Yup.

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

Post a reply to this message

Warp wrote:
>   If we express that in overly simple terms: If a rotating system consists
> of several parts, bringing those parts closer together requires energy.

Yes.

> If those parts are later pulled apart, that energy is released?

Assuming it hasn't dissipated somewhere, yes.  Think of spinning around 
an axle, reeling in a weight on a string. Now let the weight pay out, 
and you can make it do work like play a music box.

>   Or perhaps in another way: Bringing more variation to local spinning
> at different parts of the system requires energy,

I don't think the spinning and the energy are particularly connected. If 
you're talking about closed systems, the energy doesn't go away, it just 
moves around. It may move to a place (like heat) from which you can't 
move it back.

>   (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?)

I don't think that's right, no. In a closed system, you can move energy 
around but not create or destroy it. Spinning them in opposite 
directions requires moving energy from somewhere else, like a spring or 
a chemical explosion or something. In a closed system, you can't get 
them both rotating in the same direction without something else rotating 
in a different direction.

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

Post a reply to this message

Warp wrote:
>   A theoretical question: Can mass be converted to other forms of energy?

Mass *is* energy. That's where energy is stored. That's why things with 
lots of kinetic energy are heavier.  That's why a helium atom weighs 
less than four hydrogen atoms.   E=mc^2.

>   Assuming yes, how does this conversion affect angular momentum?

It doesn't. It doesn't go anywhere.  It's all the same stuff.

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

Post a reply to this message

Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> >   A theoretical question: Can mass be converted to other forms of energy?

> Mass *is* energy. That's where energy is stored. That's why things with 
> lots of kinetic energy are heavier.  That's why a helium atom weighs 
> less than four hydrogen atoms.   E=mc^2.

  That didn't really answer my question.

> >   Assuming yes, how does this conversion affect angular momentum?

> It doesn't. It doesn't go anywhere.  It's all the same stuff.

  Since angular momentum is dependent on mass, that means that eg. heat
has mass?

-- 
                                                          - Warp

Post a reply to this message

Paul Fuller <pgf### [at] optusnetcomau> wrote:
> >   Assuming yes, how does this conversion affect angular momentum?
> > 
> Simple - a photon carries angular momentum.

  Is electromagnetic radiation the only possible form of energy?

-- 
                                                          - Warp

Post a reply to this message

Warp wrote:
> Paul Fuller <pgf### [at] optusnetcomau> wrote:
>>>   Assuming yes, how does this conversion affect angular momentum?
>>>
>> Simple - a photon carries angular momentum.
> 
>   Is electromagnetic radiation the only possible form of energy?
> 
No.

Are you being obtuse ?

Let me re-phrase that.  You are being obtuse.  Is it deliberate ?

Post a reply to this message

Paul Fuller <pgf### [at] optusnetcomau> wrote:
> Warp wrote:
> > Paul Fuller <pgf### [at] optusnetcomau> wrote:
> >>>   Assuming yes, how does this conversion affect angular momentum?
> >>>
> >> Simple - a photon carries angular momentum.
> > 
> >   Is electromagnetic radiation the only possible form of energy?
> > 
> No.

> Are you being obtuse ?

> Let me re-phrase that.  You are being obtuse.  Is it deliberate ?

  Why the hell are you constantly trying to turn this into a flamewar?

  I asked if mass can be converted to other forms of energy, and if this
is so, what happens to the angular momentum. Your answer to this was that
"a photon carries angular momentum". That seems to clearly imply that all
forms of energy consist of photons. When I ask you if what you are trying
to say is that all forms of energy consist of photons you call me obtuse.

  Well, you know what? Go fuck yourself. I'm tired of your condescending
attitude.

-- 
                                                          - Warp

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