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I think that a centrifugal force F is real; it can be measured. Suppose
a ring is sliding along a rotating stick. We expect F=m*a, where a is
the ring acceleration, with respect to the stick, directed away from
the center. One can measure static F (with a calibrated spring mounted
on the stick) and one can measure the acceleration (when the ring is
allowed to slide). What is wrong with this point of view?
What is wrong is the fact that it confuses the heck out of students. The
best way to treat forces is as interactions between objects, and to only
allow the word force in that context. The centrifugal pseudo-force is only
evident in a rotating frame, but in that frame Newton's first law is
violated, unless one also presumes other pseudo-forces. But there is no
agent for the pseudo-forces, so they should not be labeled forces.
For today's students perhaps the term virtual forces should be used. This
hangs the term on virtual reality, which they understand is not real. In
either case rotating frames and pseudo-forces should not be introduced until
students have already gotten a firm grasp on interactions and NTN3. Up to
that point they always need to tell you what tangible object is causing the
interaction.
Incidentally students have difficulty in distinguishing between tangible
object and descriptive terms. Gravity is a descriptive term and the earth
is the tangible object. They have been so pumped full of terms that have no
meaning to them that they use them in place of tangible objects. This
started when in second grade they were told that gravity pulled things down.
At that point they were introduced to a magical mystical thing called
gravity. I would much prefer the phrase that things fall because the "Earth
sucks", as it at least gets the agent in there even if it promotes
misconceptions about vacuums.