Noninertial reference frame
A noninertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame.[1] An accelerometer at rest in a noninertial frame will, in general, detect a nonzero acceleration. While the laws of motion are the same in all inertial frames, in noninertial frames, they vary from frame to frame depending on the acceleration.[2][3]
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Classical mechanics 

In classical mechanics the motion of bodies in noninertial reference frames is modeled by introducing additional forces (d'Alembert forces) to inertial reference frames in order to account for the inertia effects that are appearing in this situation. Because in principle they don't belong to the modeling of an inertial frame in terms of Newton's second law such inertial effects are called fictitious forces. They might be called inertial forces or pseudo forces, too. [4] Common examples of this include the Coriolis force and the centrifugal force.
In general, the expression for any fictitious force can be derived from the acceleration of the noninertial frame.[5]
As stated by Goodman and Warner, "One might say that F = ma holds in any coordinate system provided the term 'force' is redefined to include the socalled 'reversed effective forces' or 'inertia forces'."[6]
In the theory of general relativity, the curvature of spacetime causes frames to be locally inertial, but globally noninertial. Due to the nonEuclidean geometry of curved spacetime, there are no global inertial reference frames in general relativity. More specifically, the fictitious force which appears in general relativity is the force of gravity.