Non-inertial reference frame: Difference between revisions

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A '''non-inertial reference frame''' (also known as an '''accelerated reference frame'''<ref>{{Cite web | url = https://www.ux1.eiu.edu/~cfadd/1350/06CirMtn/AccFrames.html | title=Accelerated Reference Frames | access-date=2023-09-06}}</ref>) is a [[frame of reference]] that undergoes [[acceleration]] with respect to an [[Inertial frame of reference|inertial frame]].<ref name=Tocaci>{{cite book |title=Relativistic Mechanics, Time, and Inertia |author=Emil Tocaci, Clive William Kilmister |page=251 |url=https://books.google.com/books?id=7dVRL51JRI0C&pg=PA251 |isbn=90-277-1769-9 |year=1984 |publisher=Springer }}</ref> 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.<ref>{{cite book |title=Essential Relativity |author=Wolfgang Rindler |page=25 |url=https://books.google.com/books?id=0J_dwCmQThgC&pg=PT43 |isbn=3-540-07970-X |year=1977 |publisher=[[Birkhäuser]]}}</ref><ref>{{cite book |title=Basics of Space Flight |author= Ludwik Marian Celnikier |page=286 |url=https://books.google.com/books?id=u2kf5uuaC6oC&pg=PA286 |isbn=2-86332-132-3 |year=1993 |publisher=Atlantica Séguier Frontières}}</ref>

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,<ref name=Iro>{{cite book |author=Harald Iro |title=A Modern Approach to Classical Mechanics |page=180 |url=https://books.google.com/books?id=-L5ckgdxA5YC&pg=PA179 |isbn=981-238-213-5 |year=2002 |publisher=[[World Scientific]] }}</ref> , and [[D'Alembert's principle|d'Alembert forces]]) to [[Newton's laws of motion|Newton's second law]]. Common examples of this include the [[Coriolis force]] and the [[centrifugal force (fictitious)|centrifugal force]]. In general, the expression for any fictitious force can be derived from the acceleration of the non-inertial frame.<ref name=Shadowitz>{{cite book |author=Albert Shadowitz |url=https://archive.org/details/specialrelativit0000shad |url-access=registration |title=Special relativity |isbn=0-486-65743-4 |page=[https://archive.org/details/specialrelativit0000shad/page/4 4] |publisher=[[Courier Dover Publications]] |edition=Reprint of 1968 |year=1988}}</ref> As stated by Goodman and Warner, "One might say that '''F''' {{=}} ''m'''''a''' holds in any coordinate system provided the term 'force' is redefined to include the so-called 'reversed effective forces' or 'inertia forces'."<ref name=Goodman>{{cite book |title=Dynamics |author=Lawrence E. Goodman & William H. Warner |url=https://books.google.com/books?id=2z0ue1xk7gUC |isbn=0-486-42006-X |publisher=Courier Dover Publications |year=2001 |edition=Reprint of 1963|page=358}}</ref>

In the theory of [[general relativity]], the curvature of [[spacetime]] causes frames to be [[Local reference frame|locally]] inertial, but globally non-inertial. Due to the [[Introduction to the mathematics of general relativity|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]].