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I sincerely feel that the problem with student mis-interpretations of
F_c=mv^2/r would be eliminated if, after treating the special case of
circular, constant speed motion the general case would be presented and
hammered home with copious examples (most texts don't do this). It should
then become clear that a very useful case of the (oft' used) pair
F_x=mA_x; F_y=mA_y is the pair
F_t=mdv/dt; F_c=mv^2/r;
... I can say that I have never experienced this misconception as even a
minor epidemic problem. ...