1. Nobody seem to have pointed out that not only is
"centrifugal" a perfectly good word, but that the centrifugal force
is ever-present, as the action-reaction partner of the
centripetal force. It does not, of course act on the body moving
in a circle, when viewed from an inertial frame.
2. My old first-year university textbook for Applied Mathematics
(Mechanics) has long faded from my memory, except for the page
with the diagram for circular motion. Because they had spent
many chapters on solving problems in statics, and developing all
sorts of rules and methods to apply to different situations,
they had the idea that all problems should be converted into statics
problems. So they explicitly added a fictional centrifugal
force, to counterbalance the combined centripetal effect of the
other forces present, so as to have a body in equlibrium,
and then proceeded to solve the statics problem. This is truly a
fictional force, and is the case to avoid since it makes
nonsense of the physical principles...
3. Or does it? In the accelerated frame the body *is* in
equilibrium. Just as much as my computer monitor is in equilibrium
on the table, with the "fictitious" gravitational force counter-
balancing the thrust of the table. I have become a lot less
centripetally dogmatic since starting to include the Equivalence
Principle in the course that I teach (by adopting the Cosmology
option in the IB Higher Level course). There was an article a few
years ago in Scientific American by Mark Abramovich on the unexpected
effects one experiences when orbiting a black hole, which sparked
a similar "fugal vs petal" debate. I must have another look at that
article.
Having said all that, let me add that I think it is entirely
appropriate in an introductory course to stick to the inertial
reference frame and really to emphasise that in this frame there is
no centrifugal force acting on the orbiting body.