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If students are still convinced that there is a centrifugal force somewhere
("Hey, the rope really is being held taut by *something*"), then _perhaps_
having them think about the same situation (massive object tied to the end of
a rope, the other end of the rope being held by some prime mover) for the case
of uniform linear acceleration might help. Car (or spaceship, if gravity gets
in the way) accelerates in a straight line, with something (can; astronaut)
tied to its bumper. Rope is actually held taut by the inertia of the object
(or by N3, if one reasons that way),
but in no way is there a force tugging
the rope in the opposite direction of movement from the car (or spaceship).
is the car (or spaceship) wanting to get away from the _object_.