Why does a force that doesn't exist feel so real in a turning car?

Because you're feeling your own inertia from inside a turning car. When a car enters a curve that bends to the left, you feel an apparent force pulling you to the right. Physicists call it centrifugal force and classify it as a fictitious force: one that appears only when you describe things from a rotating frame of reference. To someone watching from an overpass, nothing pulls you outward. The seat pushes you toward the inside of the curve, so that you keep moving with the car instead of carrying on in a straight line as you otherwise would. The outward 'force' you feel is the result of a centrifugal tendency caused by inertia.

Because people usually experience it from inside, on a merry-go-round or in a vehicle, centrifugal force is far better known than centripetal force. And from inside, it behaves just like a real force: in a rotating frame, every object seems pushed outward with a strength proportional to its mass, its distance from the axis and the square of the frame's rate of rotation. Yet it fails one test that real forces pass. It has no equal and opposite counterpart, so it does not obey Newton's third law.

The name is old. From 1659, the Latin term vi centrifuga, from words meaning 'fleeing from the center', appears in the notes and letters of the Dutch scientist Christiaan Huygens. When Isaac Newton received Huygens's work in 1673, he replied that this 'speculation' might prove useful in astronomy and mechanics, and in his 1687 Principia he developed the idea further. The modern view of it as a fictitious force arising in a rotating frame only took shape in the late 18th century. Engineers still use it gladly, because working in a rotating frame simplifies the analysis of centrifuges, pumps and banked curves.