Re: A rotating disk PARADOX??
From: JM Albuquerque (jm.aREMOV.E_at_sapo.pt)
Date: 07/02/04
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Date: Fri, 2 Jul 2004 18:43:40 +0100
"Bilge" wrote:
> JM Albuquerque:
> >
> >"Bilge" wrote:
> >> JM Albuquerque:
> >
> >> >The problem talks about energy conversion.
> >>
> >> I don't really care what ``the problem'' talks about. I'm not
> >> working whatever problem you are talking about. I'm answering a
> >> question about angular momentum posted to this newsgroup.
> >
> >But between the action and the reaction there is energy conversion.
> >You cannot change the problem to get rid of the energy conversion.
> >The energy conversion is the key point.
>
> It might be the ``key point'' of some problem you were assigned, but
> it doesn't have anything to do with understanding the physics of the
> question that was posted. Go reread that paragraph I wrote and try
> to figure out whether you employed any logic in your response.
Don't run away from the point.
Read the original post again:
(copy / past from the original of the thread)
----------------------------
We have a solenoid consisting of a single loop of (superconducting) wire,
generating a magnetic field. A metallic disk is in the field,
perpendicular to it, and it's being driven at constant rotational velocity.
We connect wires to the middle and edge of the disk, using sliding
contacts. There is an induced voltage between the middle and edge of the
disk, as, I believe, is well known (and even more or less agreed to in
this newsgroup). We run the wires from the disk to a resistor, and let
current flow and heat up the resistor.
In case this description isn't clear, here's a crude illustration
of the setup:
http://physicsinsights.org/images/rotating_disk_with_solenoid.png
The energy to heat the resistor comes from the motor driving the disk,
which must exert torque on the disk. Hence, the disk is also exerting an
equal and opposite torque on the motor, and there is a net transfer of
angular momentum from the disk to the Earth.
Angular momentum must be conserved. Therefore, there must be
a torque caused by the rotating disk, which is acting on the _current
ring_, and which is equal to that applied by the motor to the shaft.
---------------------------------
End.
The above clearly is the same description of Faraday's disk, also known as
the homopolar generator. It is an electromechanical machine and all
electromechanical machines convert energy between mechanical energy and
electrical energy, via an air-gap where magnetic forces act.
The homopolar generator doesn't have an air-gap, but there is energy
conversion between mechanical and electrical, via the magnetic field as
usual. Without magnetic field nothing happens.
The problem here is that it looks like you have a short vision.
The angular momentum of a disk is in fact mechanical energy stored in
the disk during time.
Quote:
The angular momentum of an isolated system remains constant in both
magnitude and direction. The angular momentum is defined as the product of
the moment of inertia I and the angular velocity. The angular momentum is a
vector quantity and the vector sum of the angular momenta of the parts of an
isolated system is constant. This puts a strong constraint on the types of
rotational motions which can occur in an isolated system. If one part of the
system is given an angular momentum in a given direction, then some other
part or parts of the system must simultaneously be given exactly the same
angular momentum in the opposite direction. As far as we can tell,
conservation of angular momentum is an absolute symmetry of nature. That is,
we do not know of anything in nature that violates it.
http://hyperphysics.phy-astr.gsu.edu/hbase/conser.html
End quote.
Hence, from the above link you can see that angular momentum conservation
Law is the same as mechanical energy conservation Law and the amount of
mechanical energy cannot be consumed during time, in the form of electricity
by mean of the Faraday's disk (an electrical generator in the case here)
without restoring that mechanical energy (by mean of a motor).
Notice again the original post from Sal:
««The energy to heat the resistor comes from the motor driving the disk,
which must exert torque on the disk. Hence, the disk is also exerting an
equal and opposite torque on the motor, and there is a net transfer of
angular momentum from the disk to the Earth.»»
You cannot have electrical energy coming from nowhere. The electrical energy
in the loop resistor converted into heat must come from a mechanical source.
The mechanical energy source is the one that gives the disk means to keep
its angular momentum and you need to supply mechanical energy to the disk
in order to have it spinning at constant angular speed (because energy is
continuously generated due to the fact that the disk is rotating and voltage
is induced).
The point is energy conversion and its conservation, not a problem of
angular momentum conservation.
There is mechanical energy involved, there is electrical energy involved and
there is an energy conversion between.
> >> Do you _really_ think batteries violate conservation of energy? That
> >> would be good news if you could prove it, but I'm wagering you can't.
> >
> >No. All that I've said is that you cannot remove the energy conversion
> >problem between action and reaction.
>
> Aside from the fact that I didn't do that, since batteries aren't magic,
> what difference does it make? Does the loop know the which ``kind'' of
> electricity is flowing? Are there different kinds of electricity?
Where is the mechanical energy then?
You give me an electrical circuit and you claim that it to be the same as an
electrical generator (the homopolar generator). You must be joking.
> >> So, are you telling me the dipole moment of the loop is not an
> >> angular momentum?
> >
> >Only if it moves. Does it move?
>
> Wrong. The dipole moment of a loop due to charges q_i moving in the loop
> at the drift velocity, v, may be written as,
Wrong?
You clearly say that it is moving.
How could a sentence like "only if it moves" be wrong when in fact it moves?
Be honest please.
> m = (1/2)\sum q_i (r_i x v_i)
>
> Since v = p/m, I can write (r x v) = (1/m)(r x p) = L/m, so
>
> m = (q/2m)L
>
> >What loop?
>
> The circuit, obviously.
>
> >Your above sentence came from nothing. Make your point first please.
>
> Since I wasn't replying to you in the first place and apparently
> you want to argue about some homework problem you were assigned
> rather than the question that was posted, I don't really care if
> you get the point. Go away.
Why?
Why do I have to go away?
> >> >And again you are wrong when you say: ««Magnetic fields do no work»»
> >> >(see the other Bilge post).
> >>
> >> No, I'm not wrong. It's trivial to show. Write down the lorentz
> >> force, F = q(E + v x B). Now write down the expression for the
> >> work, W = \integral F.dl. Insert the lorentz force into the integral,
> >> and work out the vector products. What is \integral (v x B).dl over
> >> _any_ path due to the magnetic force?
> >
> >You want to tell me that magnetic fields are conservative. OK.
>
> No, I want you read what I wrote and then sit down and try to
> understand what it means before responding.
>
> >But mathematics is not physics.
>
> Then you should let that sink in and try to understand the physics
> in the equations you use so that you stop mistaking the math for the
> physics. Don't just say it - do it.
So let me see:
F = q(E + v x B)
W = \integral F.dl
W = \integral (q (E dot L) + (v x B)).dl
Why did you delete the term \integral (q (E dot L).dl ????
Do you want to generate work from the space time curvature?
Please read some physics here about the subject above:
http://services.eng.uts.edu.au/~joe/subjects/ems/ems_ch5_nt.pdf
They clearly show that the force on the conductor carrying current i is:
Force = i (L x B)
Being L the vector electric field density, B the vector magnetic field
density and x the cross product.
> >In the real world, electrical energy is produced Worldwide based on
> >mechanical energy converted into electricity by means of energy
> >conversion that occurs in the electrical generators air-gap.
> >The air-gap consists of magnetic fluxes linked. Without magnetic fields
> >mediating the energy conversion no work could be done and for sure
> >you won't be looking at a computer screen right now.
>
> Sorry, but generators don't depend upon work done by magnetic fields.
Wrong.
The work done by the magnetic field is the same work done by the electrical
field, but they are displaced 90 degrees in time.
Can you have a continuous generation of alternating current without
involving a magnetic field? (notice I said AC, not DC).
> In a generator, there is a _changing_ magnetic field. Changing magnetic
> fields produce electric fields as faraday's law tells you:
>
> curl E = (1/c)dB/dt
>
> Electric fields do the work.
So the left side of the above equation does all the work and the right side
of the same equation does nothing. Fine, I get you physics.
And only if current is in phase with voltage.
You can have current 90 degrees out of phase with voltage and no work is
done, nevertheless current is flowing.
Just remove the magnetic field from the problem and try to see if the
generator still works.
Ever heard about energy stored by the magnetic field?
Guess what that energy is doing.
The above is the horse explanation of Faraday's Law you could provide, why?
I do know very well Faraday's Law:
V = N d(phi)/dt
Being "phi" the magnetic flux, "V" the induced voltage, "N" the number of
turns of the coil and "t" the time.
Since the new Faraday's Law depends on magnetic flux, tell me again that
magnetic fields do no work on the right side of the equation and the
electric voltage does all the work in the left side.
What Faraday's Law tells is that the work done by the electrical field is
balanced by the work done by the magnetic system against the mechanical
system. There is a mechanical system, a closed electrical circuit and a
magnetic field between both.
For instance, the open circuit has a large voltage and produces no work, nor
consumes any mechanical energy, and so the magnetic fields are not
"stressed". Next apply a short-circuit on the output. Voltage goes to near
zero, work is done in the form of heat, mechanical energy is consumed and
the magnetic field is stressed to pump the current over the circuit.
The problem with the homopolar generator is that Faraday's Law doesn't
apply. Because Faraday's Law doesn't apply you cannot see the magnetic field
at work. Notice that if you remove the magnetic field the machine doesn't
work.
Faraday's Law doesn't apply because dB/dt = 0, so d(phi)/dt = 0 and it
happens that nor V, nor E is null.
V = N d(phi)/dt
curl E = (1/c)dB/dt
Hence, the homopolar machine is a puzzlement.
Conductive materials and magnetic field cannot have relative motion,
otherwise mechanical energy is involved (created or destroyed) and work must
be done.
Without a magnetic field no work.
[...]
> >The conservation of energy is the jump made over the problem to avoid
> >a deep understanding of what is going on.
>
> Well, I think the question posted here was a little deeper than the
> one of which you seem to thinking. It was about angular momentum, not
> conservation of energy, too.
And both means the same:
http://hyperphysics.phy-astr.gsu.edu/hbase/conser.html
> >You look at mechanical side, then at the electrical side and you
> >perform a jump over the energy conversion mechanism. Those are the
> >facts.
>
> Using those ``facts'', answer the question posted regarding the torques.
> Sum the torques in the problem to get the answer, rather than using
> conservation of energy.
Because angular displacement exists and cannot be avoid, the problem is in
fact an energy conservation problem.
Energy is torque times angular displacement.
The only problem here is you short vision.
This is in fact an energy conservation problem.
Otherwise it will be free energy.
The solution of the problem is based on the energy conservation Law, not on
the angular momentum conservation Law.
http://services.eng.uts.edu.au/~joe/subjects/ems/ems_ch5_nt.pdf
I guess the point of the thread is to solve the problem, right?
> >Do you have any idea how electrical machines work?
>
> Apparently I do, in much greater detail than you seem to think
> exists.
It shows.
> >They don't work because you write down equations based on virtual work
> >(which doesn't exist).
>
> Then why do you merely write down equations and and plug in numbers
> instead of understanding the physics in the equations?
Don't confuse my posts with you posts.
You are the one writing down equations, not me.
I'm only focused in physics.
You are the one handwaving equations in the air.
> ``Virtual work'',
> is used, presumably because it avoids having to explain a lot of details
> to you about the _physics_ that don't matter for purposes of just writing
> down equations and plugging in numbers.
Physics is the art to explain the details.
Physics is not just writing down equations, because someone previously
showed that the calculation holds good, without having a single clue about
what is going on and why it works that way.
You don't want to deal with the details because you don't know the physics
to explain it with plain words (as well as equations).
> >They work because stator magnetic fields interact
> >with rotor magnetic fields, in synchronism, engaged like gear wheels,
> >based on a physical mechanism of "poles hunting poles" continuously
> >searching the point of minimum reluctance.
>
> Do you mean that you think magnet poles consciously go ``hunting'' for
> other poles and that ``reluctance'' is a ``physical thing'' because
> it has a scientific sounding name?
No, it is the way they really work.
Plot magnetic fields produced by 3-phase current versus time, around 360
degrees, and you will see poles hunting poles (repelling in nature).
Look at the working mechanism of a motor / generator conventional rotating
machine.
> Don't you think there is probably
> more physics going on than you just described?
Yes. For sure there is more physics, but I don't know that physics, like
you don't and nobody does.
The homopolar machine (the Faraday disk) is waiting for some new Einstein
that could explain why magnetic and electric fields are always balanced and
any unbalance between them causes work to be done and energy to flow.
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