Centrifugal Force

Circular motion can be analysed from two very different vantage points: (i) an inertial frame (at rest, or moving at constant velocity, watching the rotation from outside), where Newton's laws hold in their simple form; or (ii) a rotating frame (co-rotating with the object, so the object appears at rest in this frame) — a genuinely non-inertial frame, since rotation itself requires (centripetal) acceleration.

In the rotating frame, for the object to correctly appear stationary (zero net force, as Newton's laws demand when applied in this frame), an additional fictitious (pseudo) force must be introduced, exactly cancelling the real inward centripetal force: since the real force is $-m\omega^2r\,\hat r$ (inward), the pseudo force needed is $+m\omega^2r\,\hat r$ (outward) — this fictitious outward force is called the centrifugal force ("centrifugal" = "fleeing the centre").