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Re: more on non-inertial frames

On Wed, 24 Apr 1996, Rauber, Joel Phys wrote:
...
They are correct in saying that the bruise was caused by the "real" force of
the handle that stopped me, but it didn't stop me moving in a straight line
at constant speed, as measured in the non-inertial frame, (the car); but
rather stopped me from accelerated motion in a straight line, (note: I only
moved in a straight line at constant speed in the frame of reference of the
ground; my discussion is in the non-inertial frame of reference, where I
was in fact accelerating towards the car handle.)


Whether you are accelerating towards the car handle or the car handle
towards you is not an issue, nor is the frame of reference from which you
choose to view the event; what happens when the two of you come into
contact IS important. In any frame of reference, the car handle exerts
ONLY and inward (centripetal) force on you, and there is no outward
(centrifugal) force exerted on you at all; the creation of such an
outward directed centrifugal force is a sheer fiction.

Similar statements apply to the carnival ride.

These so-called "fictitious forces", which I prefer to call "kinematical"
forces or if you prefer kinematical effects (this is really symantics here),

This is no more a matter of semantics than is the TV add that presents a
75 year periodic comet as a streaking fireball. Misuse of established
terminology serves only to spread misinformation and confusion.


are indeed real effects if you choose to make measurements in non-inertial
frames of reference;

They are, of course, real accelerations; they are simply not forces,
unless one subscribes to the Queen's logic in "Alice in Wonderland," where
words mean whatever she wants them to mean. You can recall how this
confused poor Alice.


... which we do all the time and is the origin of such
comments as "the coriolis force cause the circular wind patterns prevalent
in weather systems".


The comment would be true if it said "Coriolis accelerations explain the
circular wind patterns relative to Earth's surface ...," but "Coreolis
force" does absolutely nothing, and using such a nonexistent force to
explain anything is like saying unicorn horns poke the holes in Swiss cheese.
Force has a well defined meaning, and it has none of the properties of the
kinematical quantity acceleration -- saying it does is exactly like
calling a comet a meteor.

The main difference is that the "real" forces are present in any frame of
reference, inertial or non-inertial. Whereas, the kinematical effects,
(forces)
^^^^^^^^
Why this strange insistence on calling them "forces"? The kinematical
effects being referred to have a perfectly good name: accelerations.


are not present in inertial frames of reference. Before I go on
let me hasten to make the following statement with which I think the other
viewpoint will agree; this idea of kinematic or fictitious forces being
present really comes from "mis-applying" Newtons 2nd law to a non-inertial
frame and ascribing a force to a measure acceleration multplying by mass.

Fully agreed.

I would argue that there is nothing wrong with doing this, as long as
it is UNDERSTOOD that these kinematical forces will not be present in force
diagrams in inertial frames of reference.

And as long as it is recognized that they will not do any of the things
expected of forces in ANY reference frame. Might as well declare
counterfeit money to be real in certain circumstances, and expect not to
confuse anybody.

But they must be present if you
analyze a problem in a non-inertial frame; and many problem are more easily
analyzed in such frames.

They must be present AS ACCELERATIONS (as Coriolis originally introduced
them). Why, precisely, must they be declared forces? That doesn't make
any problem one iota easier, and simply creates all the confusion this
thread is trying to undo.

...
There is nothing fictitious about the fact that in the frame of reference of
the car I am being accelerated towards the door handle before I actually
make contact with the door handle. The only way I know how to do
calculations in non-inertial frames of reference is to put in terms that
correspond to centrifugal, coriolis, azimuthal and others and treat these
"kinematical" terms as real effects and they are real effects as they in
fact contribute to the acceleration vector of a particle as measured in a
non-inertial frame of reference.

That's right, and that's the only way anyone knows how to do those
calculations -- you must include any extra accelerations that your
chosen reference frame happens to be performing, and there's nothing
particularly difficult or mysterious about this. Coriolis showed us
how to do it back in 1835 -- just don't confuse everything by renaming
the accelerations "forces," and then expecting everyone to keep doing
the mental gymnastics necessary to keep reminding themselves that these
"forces" don't have the properties that normally define forces.


I think this all comes about historically
because one measures forces on an object by first measuring the acceleration
of an object; I don't think there is any other way,

I'm completely confused by this last phrase. Am I misreading something?
Rough estimates of force can be made by your fingers and toes, or any other
part of your body.
What happened to the old fashioned bathroom scale with springs in it, or
more sophisticatedly, piezoelectric pressure meters; come to think of it,
the very sensitive Cavendish balance for measuring G doesn't depend on
measuring accelerations -- it doesn't matter how quickly or slowly the
balance rotor comes to rest, just how much torsion there is at the end
in the supporting fiber. Acceleration is a purely kinematical quantity,
measured in terms of relative position and time, which in itself has
nothing to do with the forces experienced or measured. In fact, it
precisely took the genius of Newton to sort things out enough to see
that there is any relation between force and acceleration at all, and
then the relation only shows up in certain reference frames.

force balances work
implicitly by first measureing a zero acceleration.


Sorry, but force balances are zeroed by registering zero force (o
zero pressure = force/area); it has nothing to do with acceleration.
(Step on a spring balance fast -- as long as you don't exceed the
spring limit and break the scale -- or slow, you're not going to
affect the final reading on your weight; in fact you have to wait
until any oscillations you may have set up have died out completely
before you can get any reading on your weight.)

There is a body of opinion that wants to expunge the word "centrifugal" and
I assume by analogy "coriolis" from the physics vocabulary; presumably for
the reason that they don't belong when dealing with inertial frames of
reference.

I hope that opinion doesn't win out -- the terms "centrifugal,"
"centripetal," "Coriolis" are perfectly accurate when describing the
corresponding accelerations, and "centrifugal" and "centripetal"
can certainly be used of forces directed away from or toward a center.
It would be a shame to lose these terms from our vocabulary. It's like
saying we should abandon the term "comet" because so many people confuse
it with "meteor."

But they do belong in the terminology when discussing
calculations done in non-inertial frames of reference.

They certainily do -- just use them as adjectives describing the
corresponding accelerations, and there's no problem whatsoever.

So argue to keep the
terminology; although as a matter of practice in my introductory classes I
stick to inertial frames of reference and "forbid" the use of "centrifugal"
and stick to "centripetal".

That seems strange, since it's the term "force" used instead of
"acceleration" that causes the problems. I don't really see any
reason for proscribing either of the above listed terms, just don't
call an acceleration a force, and don't misuse the terms, such as
by saying there is a centrifugal force present when actually the
force acting is centripetal, Etc.

The reasons are pedagogical, as I don't want to
confuse the issue (the 2nd law is hard enough as it is); which is easily
done, even when discussers are agreeing. My comments are points that I only
bring up in advanced classes.


I find that the big pedagogical necessity that must REALLY, REALLY be
emphasized (but often isn't) is to preface every statement of Newton's
laws with the necessary condition "RELATIVE TO AN INERTIAL REFERENCE
FRAME ... ." Then the laws are true, otherwise they are not.

BTW to others reading these and the respondent comments, I'm willing to bet
that both me and my respondents (to whom I thank for the comments, I
intended to stimulate discussion of this) will get the same answers when we
work and analyze problems and in this sense the discussion is about
symantics (or even philosophical).


To close with an astronomical question, can you see a way to get the
quantity (M+m) in Newton's corrected version of Kepler's Third Law by
introducing extra "kinematical forces" in the noninertial frame in which
Earth and Sun are at rest? That was a claim that was made in another
post, but so far not fulfilled.

A. R. Marlow E-MAIL: marlow@beta.loyno.edu
Department of Physics PHONE: (504) 865 3647 (Office)
Loyola University 865 2245 (Home)
New Orleans, LA 70118 FAX: (504) 865 2453