A non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will in general detect a non-zero acceleration. In a curved spacetime all frames are non-inertial. The laws of motion in non-inertial frames do not take the simple form they do in inertial frames, and the laws vary from frame to frame depending on the acceleration. To explain the motion of bodies entirely within the viewpoint of non-inertial reference frames, fictitious forces (also called inertial forces, pseudo-forces and d'Alembert forces) must be introduced to account for the observed motion, such as the Coriolis force or the centrifugal force, as derived from the acceleration of the non-inertial frame. 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 so-called 'reversed effective forces' or 'inertia forces'."
Read more about Non-inertial Reference Frame: Avoiding Fictitious Forces in Calculations, Detection of A Non-inertial Frame: Need For Fictitious Forces, Fictitious Forces in Curvilinear Coordinates
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