Non-inertial reference frame: Difference between revisions

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{{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&dq=isbn=0201565188 |isbn= 0-201-56518-8}}</ref> 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.<ref name=Price>“The inertial frame equations have to account for ''V_Ω'' 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}}

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==Detection of a non-inertial frame: need for fictitious forces==

That a given frame is non-inertial can be detected by its need for fictitious forces to explain observed motions.<ref name=Serway>{{cite book |title=Physics for scientists & engineers |author=Raymond A. Serway |year=1990 |publisher=Saunders College Publishing |edition=3rd |isbn=0-03-031358-9 |page=135 |url=https://books.google.com/books?lr=&as_brr=0&q=%22fictitious+forces+do+not+exist+when+the+motion+is+observed+in+an+inertial+frame.+The+fictitious+forces+are+used+only+in+an+accelerating%22&btnG=Search+Books}}</ref><ref name="ArnoldQuote">{{cite book |title=Mathematical Methods of Classical Mechanics |page=129 |author=V. I. Arnol'd |isbn=978-0-387-96890-2 |year=1989 |url=https://books.google.com/books?as_q=&num=10&btnG=Google+Search&as_epq=additional+terms+called+inertial+forces.+This+allows+us+to+detect+experimentally&as_oq=&as_eq=&as_brr=0&lr=&as_vt=&as_auth=&as_pub=&as_sub=&as_drrb=c&as_miny=&as_maxy=&as_isbn=|publisher=Springer}}</ref><ref name=Rothman>{{cite book |title=Discovering the Natural Laws: The Experimental Basis of Physics |author= Milton A. Rothman |page=[https://archive.org/details/discoveringnatur0000roth/page/23 23] |url=https://archive.org/details/discoveringnatur0000roth

|url-access=registration |quote=reference laws of physics. |isbn=0-486-26178-6 |publisher=Courier Dover Publications |year=1989 }}</ref><ref name=Borowitz>{{cite book |title=A Contemporary View of Elementary Physics |page=138 |publisher=McGraw-Hill |year=1968 |url=https://books.google.com/books?as_q=&num=10&btnG=Google+Search&as_epq=The+effect+of+his+being+in+the+noninertial+frame+is+to+require+the+observer+to&as_oq=&as_eq=&as_brr=0&lr=&as_vt=&as_auth=&as_pub=&as_sub=&as_drrb=c&as_miny=&as_maxy=&as_isbn= |asin= B000GQB02A |author=Sidney Borowitz & Lawrence A. Bornstein }}</ref><ref name=Meirovitch>{{cite book |author=Leonard Meirovitch |page=4 |isbn=0-486-43239-4 |publisher=Courier Dover Publications |year=2004 |edition=Reprint of 1970 |url=https://books.google.com/books?id=GfCil84YTm4C&pg=PA4&dq=%22in+accelerated+systems,+we+must%22&pg=PA4 |title =Methods of analytical Dynamics}}</ref> For example, the rotation of the [[Earth]] can be observed using a [[Foucault pendulum]].<ref name=diFrancia>{{cite book |title=The Investigation of the Physical World |author=Giuliano Toraldo di Francia |page=115 |url=https://books.google.com/books?id=cFQ7AAAAIAAJ&pg=PA46&dq=laws+physics+%22+form%22#PPA115,M1&pg=PA46 |isbn=0-521-29925-X |publisher=[[CUP Archive]] |year=1981 }}</ref> The rotation of the Earth seemingly causes the pendulum to change its plane of oscillation because the surroundings of the pendulum move with the Earth. As seen from an Earth-bound (non-inertial) frame of reference, the explanation of this apparent change in orientation requires the introduction of the fictitious [[Coriolis effect|Coriolis force]].

Another famous example is that of the tension in the string between [[rotating spheres|two spheres rotating about each other]].<ref>