Content deleted Content added
HeyElliott (talk | contribs) m MOS:CQ |
TeyeJohn2000 (talk | contribs) No edit summary |
||
Line 2:
{{Expand Spanish|Sistema de referencia no inercial|date=September 2022}}
{{Classical mechanics}}
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]].
Line 10:
==Avoiding fictitious forces in calculations==
{{see also|Inertial frame of reference|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.<ref name=Alonzo>{{cite book |author=M. Alonso & E.J. Finn |title=Fundamental university physics |publisher=Addison-Wesley |year=1992 |url=https://books.google.com/books?id=c5UAAAAACAAJ |isbn=0-201-56518-8 }}{{Dead link|date=November 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> This approach avoids the 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.<ref name=Price>"The inertial frame equations have to account for ''V<sub>Ω</sub>'' and this very large centripetal force explicitly, and yet our interest is almost always the small relative motion of the atmosphere and ocean, ''V' '', since it is the relative
motion that transports heat and mass over the Earth. … To say it a little differently—it is the relative velocity that we measure when [we] observe from Earth’s surface, and it is the relative velocity that we seek for most any practical purposes." [http://ocw.mit.edu/ans7870/resources/price/index.htm MIT essays] by James F. Price, Woods Hole Oceanographic Institution (2006). See in particular §4.3, p. 34 in the [http://ocw.mit.edu/ans7870/resources/price/essay2.pdf Coriolis lecture]</ref> As pointed out by Ryder for the case of rotating frames as used in meteorology:<ref name=Ryder>{{cite book |title=Classical Mechanics |author=Peter Ryder |url=https://books.google.com/books?id=j1Y5FfdQHsQC&pg=PA80 |isbn=978-3-8322-6003-3 |publisher=Aachen Shaker |year=2007 |pages=78–79 }}</ref>
{{quote|A simple way of dealing with this problem is, of course, to transform all coordinates to an inertial system. This is, however, sometimes inconvenient. Suppose, for example, we wish to calculate the movement of air masses in the earth's atmosphere due to pressure gradients. We need the results relative to the rotating frame, the earth, so it is better to stay within this coordinate system if possible. This can be achieved by introducing ''fictitious'' (or "non-existent") forces which enable us to apply Newton's Laws of Motion in the same way as in an inertial frame.|Peter Ryder|''Classical Mechanics'', pp. 78-79}}
Line 19:
Another famous example is that of the tension in the string between [[rotating spheres|two spheres rotating about each other]].<ref>
{{cite book |title=Analytical Mechanics |page=324 |url=https://books.google.com/books?id=1J2hzvX2Xh8C&pg=PA324 |isbn=0-521-57572-9 |publisher=[[Cambridge University Press]] |year=1998 |author=Louis N. Hand, Janet D. Finch}}</ref><ref>{{cite book |title=The Cambridge companion to Newton |url =https://books.google.com/books?id=3wIzvqzfUXkC&pg=PA43 |author=I. Bernard Cohen, George Edwin Smith |page=43 |isbn=0-521-65696-6 |year=2002 |publisher=Cambridge University Press}}</ref> In that case, the prediction of the measured tension in the string based
In this connection, it may be noted that a change in coordinate system, for example, from Cartesian to polar, if implemented without any change in relative motion, does not cause the appearance of fictitious forces,
==Fictitious forces in curvilinear coordinates==
Line 34:
===Frames and flat spacetime===
{{See|Proper reference frame (flat spacetime)}}
If a region of spacetime is declared to be [[Euclidean space|Euclidean]], and effectively free from obvious gravitational fields, then if an accelerated coordinate system is overlaid onto the same region, it can be said that a ''uniform fictitious field'' exists in the accelerated frame (we reserve the word gravitational for the case in which a mass is involved). An object accelerated to be stationary in the accelerated frame will "feel" the presence of the field, and they will also be able to see environmental matter with inertial states of motion (stars, galaxies, etc.) to be apparently falling "downwards" in the field
In frame-based descriptions, this supposed field can be made to appear or disappear by switching between "accelerated" and "inertial" coordinate systems.
| |||