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Concept
Non-inertial reference frame
Summary
A non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame. 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.
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 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. 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'."
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.
Inertial frame of reference and Fictitious force
In flat spacetime, the use of non-inertial frames can be avoided if desired. Measurements with respect to non-inertial reference frames can always be transformed to an inertial frame, incorporating directly the acceleration of the non-inertial frame as that acceleration as seen from the inertial frame. This approach avoids use of fictitious forces (it is based on an inertial frame, where fictitious forces are absent, by definition) but it may be less convenient from an intuitive, observational, and even a calculational viewpoint. As pointed out by Ryder for the case of rotating frames as used in meteorology:
A simple way of dealing with this problem is, of course, to transform all coordinates to an inertial system.
Official source
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