Re: NIF: the power company

[Bowman_David/tiger_mpc@tiger.gtc.georgetown.ky.us]

Up until now I have stayed out of the noninertial frame effects discussion
because, like many, I think that, for the most part, a distinction without a
difference is being made concerning what to call these noninertial frame
effects. I think the argument is over a matter of words rather than physics.
I don't particularly care if, when working in a noninertial frame, I say that
I'm applying N2 and treating the noninertial effects as fictitious, pseudo,
apparent, kinematic, reference frame generated, etc. forces, or whether I say
that N2 is not true and that extra acceleration correction terms need to be
added to the equations to properly describe the physics and thereby spoil the
validity of N2.  If this is all that was being said in this argument I would
have stayed out of it.  However A. Marlow has said some things about some real
forces that I think are, at best, misleading and need correction or, at 
least, clarification.

A. M. said:
>                   ...  or you can tie a magnet to the cat's tail and 
> measure the forces near your local hospital's magnetic resonance imaging
> equipment.  Everyone agrees these are real forces and we make them do 
> real work for us all the time.
I don't agree.  Magnetic *forces* do NO work.  The magnetic force on a charged
particle is always perpendicular to the particle's motion thereby giving zero
for the line integral giving the work done on the particle.  Magnetic fields
CAN do work via *torques* NOT *forces* on permanent magnetic dipole moments
(such as a charged elementary particle with an intrinsic spin or a magnet tied
to a cat's tail).

> If we lived on such a planet we probably would not be having this discussion,
> since everyone all the time would have to cope with the very noticeable 
> effects, and a clear understanding of them would be part of every curriculum
> from the earliest grades.  For example, plumb lines would very noticeably 
> deviate from the vertical (= right angle to planet's surface), and to make
> them hang vertically a significant force (as measured by a spring scale) 
> would have to be applied.
Actually (if the planet spun slowly enough for the planet to hang together)
plumb lines would NOT deviate from vertical as vertical is DEFINED as the
direction that a plumb bob would hang (when in equilibrium--at rest in the
frame rotating with the planet's surface).  Also the planet's surface would
also be perpendicular to this vertical direction (except for some possible
small scale imperfections such as hills, valleys, and ocean waves).

> ...
> And yes, I suspect energy would be much cheaper on such a planet, since 
> it would be so easy to extract it from the obvious acceleration of their 
> planet's surface relative to inertial axes.  But again no one would be 
> deceived as to the source of such energy  --  they would clearly be 
> extracting it from the rotational energy of their planet.  (Wind mills,
> of course, would be a very easy way of harnessing their planet.)
Assuming one does not count as extracting this energy doing globally   
significant things such as raising the gravitational potential energy of
interaction between the planet and its moon by having tidal effects spiral
the moon outward from the planet, then I disagree that such energy could be
extracted.  In any case the extraction, if one did allow the above case, would
certainly not be *easy* nor technologically useful.  One would then need to
figure how to extract useful energy from the continuously receding moon.  The
reason that easy energy could not be extracted is that the effects of the
acceleration of the rotating coordinate system can't  *by themselves* do work
(I guess Marlow might call it pseudowork anyway) on objects near the planet's
surface.  The centrifugal effect (relative acceleration, fictitious force,
etc.) can be seen to be due to a simple conservative (pseudo)potential in the
rotating frame and it just adds to the gravitational (pseudo)potential already
present due to planet's mass, and the combined effect of the two is to just
give the planet a non-spherically (but axially) symmetric effective-
gravitational geoid.  Since the planet's surface will already be coincident
with a surface of constant geopotential from the time of its earliest
formation we could not extract energy by rolling extra mass "down hill".  As  
far as the planet's Coriolis effect (relative acceleration, fictitious force,
etc.) can be seen to be a magnetic-like velocity-dependent (pseudo)force which
acts perpendicularly to an object's motion thus zeroing out any possible
pseudo-work.  Forces which change an object's direction but not its speed do
no work. Thus the Coriolis acceleration cannot be harnessed to extract any of
the kinetic energy bound up in the planet's rotation.  IF the planet had an
atmosphere, or at least a low viscosity ocean (with a temperature, salinity,
or pressure dependent density) then energy COULD be extracted from the wind,
the storms or ocean the currents with possible windmill-turbine-type devices.
If the planet was orbiting close enough to a star to heat it and if the spin
axis were properly oriented relative to the planet's ecliptic plane then the
large spin rate would make for some nasty storm systems-and potent surface
currents.  Much energy could be extracted from all this fluid motion, BUT NONE
of it would come from the planet's rotational kinetic energy.  Rather it would
come from the central star's radiation as it heats the planet and thus powers
the planet's heat engine of surface fluid currents.

David Bowman
Georgetown College
dbowman@gtc.georgetown.ky.us