Two short and one long comment and reference.
1. Pedagogically, Inertial Reference Frames should be used at the
introductory course level. "Centrifugal" and other fictitious forces
should be avoided.,
2. Like the analogy with GR and the falling elevator, the rotating coordinate
system results in a simplification only for a restricted region of space so
that the acceleration appears uniform.
3. I don't recall a reference to the long history of this debate, probably
beginning with D'Alembert.
Arnold Sommerfeld's "Mechanics" (1952 Academic Press edition - which says
it is translated from the German edition of 1944) section 10 is entitled:
"D"Alembert's Principle; Introduction of Inertial Forces"
Selected quotes -
" As we have seen, all bodies have a tendancy to remain in a state of rest
or of uniform rectilinear motion. We can think of this tendancy as a
resistance to changes in the motion, an inertial resistance, or, for
brevity, as an _inertial_force_. The definition of inertial force F* for
the single mass point is therefore
(1) F* = - dp/dt (p dot)
and the fundamental law dp/dt = F takes on the form
(2) F* + F = 0
The inertial force is in vectorial equilibrium with the applied force.
While F is a forcer given by the physical situation, F* is a fictitious
force. We introduce it in order to reduce problems of motion to problems
involving equilibrium, a procedure that is often convenient."
--------------------
" Strangely enough, the great Heinrich Hertz raises objections to the
intriduction of the centrifugal force in the unusually beautiful and beautifull
y written introduction to his "Mechanics":
"We swing a stone attached to a string in a circle; we thereby consciously
exert a force on the stone ; this force constantly deviates the stone from a
straight path, and if we alter this force, the mass of the stone or the length
of the string, we discover that indeed the motion of the stone occurs at all
times in agreement with Newton's second law. Now the third law demands a force
opposing that which is exerted by our hand on the stone. If we ask for this
force, we obtain the answer familiar to everybody, that the stone reacts on the
hand by virtue of the centrifugal foce, and that this centrifugal force is
indeed equal and opposite to the force exerted on us by the stone. Is this
mode of expression admissable? Is that which we now call centrifugal force
anything but the inertia of the stone?"
We answer this question with a flat no; indeed the centrifugfal force;
by virtue of our definition (3), is identical to the inertia of the stone.
But the foirce opposing that which we exert on the stone, ie, really on the
string, is the pull which the string exerts on our hand. Hertz further
remarks that "we are forced to the conclusion that the classification of the
centrifugal force as a force is not suitable; its name, just like that of
live force, is to be regarded as a heritage passed down from former times;
and from the point of view of usefulness the retention of this name is easier
to excuse than to justify." In regard to this we would like to say that the
name centrifugal force needs no justification, for it rests, liker the more gen
eral term, inertial force, on a clear definition.
Incidentally, it is precisely this alleged lack of clarity of the force
concept which induced Hertz, in an interesting but not very fruitful attempt,
to construct his mechanics without the notion of foce.
We now come to the achievement of d'Alembert (mathematician, philosopher,
astronomer, physicist, encyclopedist; "Traite de Dynamique", 1758)."