Main Question or Discussion Point
The (perfect) circle, defined in the Cartesian coordinates as the set of (x,y) pairs that fit the equation x^2 + y^2 = r^2 can "exist" as a mathematical abstraction, I have no problem with that. But can we have a perfect circle in the physical world? Particularly, can an object move in a perfectly circular path? The way I see it, for the object to move in such a way it would have to change direction an infinite amount of times per cycle. Even in a fraction of a cycle it would have to change direction an infinite amount of times; isn't this a logical impossibility? Can we have perfect circular MOTION?