more on non-inertial frames

["Rauber, Joel Phys" <RAUBERJ@mg.sdstate.edu>]

One respondent wrote,
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Your arm may be bruised, but that IS from a real force, the force of the
door handle that stopped you from moving off along the straight line path
you were taking (N1).  In the rotor ride, again there IS no outward force,
only the inward force of the wall--again keeping you from moving in a
straight line.  The problem with using human sensations 'to define' forces
in these situations, is that we have come to experience MANY forces
BACKWARDS!
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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.)

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), 
are indeed real effects if you choose to make measurements in non-inertial 
frames of reference; 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 main difference is that the "real" forces are present in any frame of 
reference, inertial or non-inertial.  Whereas, the kinematical effects, 
(forces) 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 multiplying by mass. 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.  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.

Another respondent said,
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You have it correct here, if you mean that it is the real inward directed
centriPETAL forces that cause the bruises, Etc., but you also have them
somehow balancing the "kinematical" forces.  What are these outward
directed centrifugal "kinematical" forces doing?   The answer is: nothing!
They don't exist, which is why they cause no effects, which is why they are
called fictitious.

> ... In other words, I'm saying that we actually "feel" these forces,
> therefore the term "fictitious" is somewhat of a misnomer.

Sorry, but the term "fictitious" is not at all a misnomer when applied to
the psychologically created outward directed centrifugal force in the
examples you cited.  We do not feel these forces.  What we feel is the
inward directed (i. e., centripetal) pressure on our skin, and this is
all that exists.
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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. 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, force balances work 
implicitly by first measureing a zero acceleration.

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

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).

Thanks for reading this horribly long note from a reader who lives and 
experiences the world a non-inertial frame of reference (particularly when I 
drive too fast around a curve).  I could easily add more, but I'll restrain 
myself.

Joel Rauber
rauberj@mg.sdstate.edu