Centrifugal force

Centrifugal force is not a real force. It is a bookkeeping term that appears when you write Newton's second law in a rotating frame of reference. The true force on a body moving in a circle points inward (the centripetal force); an observer rotating with the body, however, sees the body apparently pushed outward, and to make Newton's laws work from that observer's point of view you add a fictitious outward force of magnitude mΩ²r. That force is called centrifugal.

You feel something centrifugal-like every time a car takes a sharp turn. In the road's frame, the only real horizontal force on you is the inward push of your seat belt and the seat's friction. In your own frame — which is rotating with the car — you feel as if you are being thrown outward, because your body wants to continue in a straight line and the car is pulling you off that line. Call that sensation centrifugal if you like; it is the fictitious force needed to explain your apparent acceleration from inside the turning car.

The same accounting trick explains the slightly flattened shape of the Earth (spinning Earth + effective centrifugal potential makes the equator bulge), the water rising up the walls of a spinning bucket (Newton's famous thought experiment), and why a space station has to spin to simulate gravity: in the rotating frame of the station, centrifugal force pulls you toward the outer wall, and that becomes your local "down."

Christiaan Huygens introduced the Latin phrase vis centrifuga (fleeing-the-center force) in his 1659 manuscript De Vi Centrifuga, computing its magnitude as mΩ²r nearly thirty years before Newton's Principia. Newton reused the term but reconceived centripetal (seeking-the-center) as the physically real force; "centrifugal" survived only as the fictitious counterpart in rotating frames.