Re: Centrifugal Force

["A. R. Marlow" <marlow@loyno.edu>]

On Sat, 21 Feb 1998, David Bowman wrote:

> ...
> I don't know if it is so much a commitment to inventing mystical forces, as
> it is the absence of a rigid doctrinaire commitment to one particular
> absolute true definition of a true force.

Ah, and all this time I thought a single definition would be useful.  But
no one is saying definitions have truth value, I hope.  I have repeatedly
said definitions are free, but it seems to me we should settle on one if
we are to communicate among ourselves and to our students.  It seems to me
that force is too important and fundamental a physical concept to be left
in the murky state being proposed. 

> It is rather a holding to a looser
> concept of a force based on utility and functional role in the mathematics
> of a given description of the situation.

I see.  This is very illuminating, and clears up exactly where the
difficulty has been in all this lengthy discussion.  We must allow a
looser concept of force.  That should clear up all the other discussions
going on, too.  Allow a looser concept of current, charge, mass, weight,
Etc.  It is a great problem solver.

  Actually, it is the invention of
> those extra forces that keeps things a little *more* Newtonian than
> otherwise in accelerated frames.  Not calling the frame-induced effects
> forces results in both Newton's first and second laws being violated 

A pedagogical question: Do you not introduce Newton's laws I & II to your
physics majors  with the qualification "relative to an inertial frame"
included?  If not, when do they discuss inertial frames, and how do they
distinguish them from other frames?  If you do include such a
qualification (and I obviously do), then not calling frame-induced
accelerations forces results in no violation of the laws.

> is not the case when doing problems involving Newtonian gravitation,
> however.  When analysing orbital mechanics problems it is simplest to treat
> the problem from a (noninertial) frame where the massive body is at rest and
> is considered a source of a (locally fictitious on a small scale)
> gravitational field, rather than treat the orbits of objects in a frame in
> which those objects are unaccelerated in free fall.  Certainly analysing the
> behavior of atmospheric and oceanic currents in meteorology and oceanography
> is easiest in noninertial frame in which the earth's surface is at rest.
  
To clear up what seems to be a point of confusion:  no one is advocating
not using noninertial frames.  They are great frames for many problems.
But using such frames does not at all require mislabeling accelerations as
forces.  The actual forces present are quite sufficient to explain
everything.  In the examples you cite, the force of the wind or water
pushing on you, the force of the earth on your feet, both forces working
mightily to try and topple you, and both having clear third law
counterparts.  Where is there room for any additional force?  (Unless, of
course, loose definitions are invoked, in which case anything goes.)

I thought progress was being made, but now I'm not so sure.  When a "quack
test" for forces was proposed, I got my hopes up, because that usually is
very easy to apply.  But when I saw that the proposed test allowed
Coriolis acceleration to masquerade as force, even though it has been
agreed that a) it does no work, b) it has no third law counterpart, and c)
it does not cause anything to deviate from inertial motion, my hopes were
dashed.  To teach such would be like teaching students to call a cat a
duck, even though the feline does not waddle, has no feathers and can't
quack.  

The argument does in the end seem to be over definitions --  apparently
whether they should be loose or not  --  and I conclude there is still a
lot of room for advancement in the fundamentals of our profession.


A. R. Marlow                          E-MAIL:  marlow@loyno.edu
Department of Physics, Box 124        PHONE:   (504) 865 3647  (Office)  
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