Non-inertial reference frame

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${\displaystyle {\textbf {F}}={\frac {d}{dt}}(m{\textbf {v}})}$ Second law of motion
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A non-inertial reference frame (also known as an accelerated reference frame^[1]) is a frame of reference that undergoes acceleration with respect to an inertial frame.^[2] An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion are the same in all inertial frames, in non-inertial frames, they vary from frame to frame depending on the acceleration.^[3][4]

In classical mechanics it is often possible to explain the motion of bodies in non-inertial reference frames by introducing additional fictitious forces (also called inertial forces, pseudo-forces^[5] and d'Alembert forces) to Newton's second law. 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 non-inertial frame.^[6] 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'."^[7]

In the theory of general relativity, the curvature of spacetime causes frames to be locally inertial, but globally non-inertial. Due to the non-Euclidean geometry of curved space-time, 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.