Non-inertial frames and fictitious forces

Newton's second law, F = ma, is exactly true only in inertial frames — those moving at constant velocity, with no acceleration of their own. An observer who is themselves accelerating, like a passenger in a braking car, or rotating, like someone standing on a carousel, finds that objects around them appear to accelerate in ways F = ma cannot explain using only the real forces present. Rather than abandon Newton's law, physics keeps the equation and adds a correction term — a fictitious force, equal to minus the frame's own mass times its acceleration, that exists purely as a bookkeeping device for describing motion from within an accelerating viewpoint.

"Fictitious" describes where the force comes from, not whether its effects are real. A passenger thrown against their seatbelt when a car brakes suddenly experiences a completely real deceleration; the seatbelt exerts a completely real force. What is fictitious is attributing that to some force pushing the passenger forward — from the road's inertial frame, nothing pushes the passenger at all. Their body's inertia simply keeps it moving at the car's original speed while the car (and the seatbelt) decelerates around them, and the seatbelt's very real force is what then decelerates the passenger too.

The centrifugal force on a spinning carousel is the same story. From the ground, the actual physics is straightforward: friction (or a handrail) supplies a real, inward centripetal force that keeps the rider moving in a circle, precisely as centripetal force always works. From the rider's own rotating viewpoint, there is no such inward force apparent — they feel stationary — so an outward centrifugal force has to be invented to explain why they still feel pressed against the outer edge. Both descriptions predict the same physical outcome; they differ only in which frame does the accounting, and switching frames is exactly what makes the "extra" force appear or vanish.