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Non-inertial reference frame

A non-inertial reference frame is a frame that is not an inertial reference frame. As such, the laws of physics in such a frame do not take on their most simple form, as required by the special principle of relativity. 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.

Of course, measurements with respect to non-inertial reference frames can be transformed to a convenient inertial frame, incorporating directly the acceleration of the non-inertial frame as that acceleration is 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 and even a calculational viewpoint. As pointed out by Ryder for the case of rotating frames as used in meteorology:

That a given frame is non-inertial can be detected by its need for fictitious forces to explain observed motions. For example, the rotation of the Earth can be observed using a Foucault pendulum. The rotation of the Earth causes the pendulum to change its plane of oscillation with respect to its surroundings. The explanation of this behavior from an Earth-bound (non-inertial) frame of reference requires the introduction of the fictitious Coriolis force.

Another famous example is that of the tension in the string between rotating spheres. In that case, prediction of the measured tension in the string based upon the motion of the spheres as observed from a rotating reference frame requires the rotating observers to introduce a fictitious centrifugal force .

In general, the identification of a frame as non-inertial is established by the presence of fictitious forces. Arnol'd says: As stated by Iro: