Here's the definition:
centrifugal force (sen-trif-yuh-guhl, sen-trif-uh-guhl)
A force that tends to move objects away from the center in a system undergoing circular motion. Centrifugal force keeps the water in a whirling bucket from spilling or throws a rider in a car against the door when the car goes around a sharp curve. Centrifugal force is actually a form of inertia.
Frankly, I can't see where it's worth my time to argue something that anyone with a basic physics background would just shrug and smile at. There is no "centrifugal force"... what you feel is an object attempting to maintain it's straight-line direction (Newton's First Law, I believe) while you try to contain it in rotational movement. That is not a force that requires a special name, as people mistakenly did for a while.... that is inertia at work. Should we rigorously derive the equations so there's no question?