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Talk:Centrifugal force (rotating reference frame) - Wikipedia

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vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#More_properly_an_effect_than_a_force?"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>More properly an effect than a force?</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">3 comments</span> <ul id="toc-More_properly_an_effect_than_a_force?-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Acceleration_Derivation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Acceleration_Derivation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Acceleration Derivation</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">2 comments</span> <ul id="toc-Acceleration_Derivation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-It&#039;s_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_the_frame." class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#It&#039;s_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_the_frame."> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>It's the rotation of the <i>direction of the velocity vector</i> that matters, not of the frame.</span> </div> </a> <span class="ext-discussiontools-init-sidebar-meta">1 comment</span> <ul id="toc-It&#039;s_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_the_frame.-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" 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font-size:11.9px;"> <hr/> This page has archives. Sections older than <b>90 days</b> may be automatically archived by <span class="nowraplinks"><a href="/wiki/User:Lowercase_sigmabot_III" title="User:Lowercase sigmabot III">Lowercase sigmabot III</a></span> when more than 4 sections are present.</td></tr> </tbody></table> <meta property="mw:PageProp/toc"/> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><!--__DTSUBSCRIBEBUTTONDESKTOP__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-Kvng-2012-07-02T20:46:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-Not_to_be_confused_with-2012-07-02T20:46:00.000Z&quot;,&quot;replies&quot;:[&quot;c-Kvng-2012-07-02T20:46:00.000Z-Not_to_be_confused_with&quot;],&quot;text&quot;:&quot;Not to be confused with&quot;,&quot;linkableTitle&quot;:&quot;Not to be confused with&quot;}--><h2 id="Not_to_be_confused_with" data-mw-thread-id="h-Not_to_be_confused_with-2012-07-02T20:46:00.000Z"><span data-mw-comment-start="" id="h-Not_to_be_confused_with-2012-07-02T20:46:00.000Z"></span>Not to be confused with<span data-mw-comment-end="h-Not_to_be_confused_with-2012-07-02T20:46:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Centrifugal_force_(rotating_reference_frame)&amp;action=edit&amp;section=1" title="Edit section: Not to be confused with"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><!--__DTELLIPSISBUTTON__{"threadItem":{"headingLevel":2,"name":"h-Kvng-2012-07-02T20:46:00.000Z","type":"heading","level":0,"id":"h-Not_to_be_confused_with-2012-07-02T20:46:00.000Z","replies":["c-Kvng-2012-07-02T20:46:00.000Z-Not_to_be_confused_with"]}}--><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"><!--__DTLATESTCOMMENTTHREAD__{"id":"c-Kvng-2012-07-02T20:46:00.000Z-Not_to_be_confused_with","timestamp":"2012-07-02T20:46:00.000Z"}__--><!--__DTCOMMENTCOUNT__1__--><!--__DTAUTHORCOUNT__1__--></div><div class="ext-discussiontools-init-section-actions"><!--__DTSUBSCRIBEBUTTONMOBILE__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-Kvng-2012-07-02T20:46:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-Not_to_be_confused_with-2012-07-02T20:46:00.000Z&quot;,&quot;replies&quot;:[&quot;c-Kvng-2012-07-02T20:46:00.000Z-Not_to_be_confused_with&quot;],&quot;text&quot;:&quot;Not to be confused with&quot;,&quot;linkableTitle&quot;:&quot;Not to be confused with&quot;}--></div></div></div> <p><span data-mw-comment-start="" id="c-Kvng-2012-07-02T20:46:00.000Z-Not_to_be_confused_with"></span>There are various warnings not to confuse various forces: <a href="/wiki/Centrifugal_force" title="Centrifugal force">Centrifugal force</a>, <a href="/wiki/Reactive_centrifugal_force" title="Reactive centrifugal force">Reactive centrifugal force</a>, <a href="/wiki/Centripetal_force" title="Centripetal force">Centripetal force</a>, <a href="/wiki/Centrifugal_force_(rotating_reference_frame)" class="mw-redirect" title="Centrifugal force (rotating reference frame)">Centrifugal force (rotating reference frame)</a>. There is however no discussion of the distinction between these various phenomenon. --<a href="/wiki/User:Kvng" title="User:Kvng">Kvng</a> (<a href="/wiki/User_talk:Kvng" title="User talk:Kvng">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Centrifugal_force_(rotating_reference_frame)#c-Kvng-2012-07-02T20:46:00.000Z-Not_to_be_confused_with" class="ext-discussiontools-init-timestamplink">20:46, 2 July 2012 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Kvng-2012-07-02T20:46:00.000Z-Not_to_be_confused_with"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2012-07-02T20:46:00.000Z","author":"Kvng","type":"comment","level":1,"id":"c-Kvng-2012-07-02T20:46:00.000Z-Not_to_be_confused_with","replies":[]}}--></span><span data-mw-comment-end="c-Kvng-2012-07-02T20:46:00.000Z-Not_to_be_confused_with"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><!--__DTSUBSCRIBEBUTTONDESKTOP__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-PaulTanenbaum-2013-02-19T20:57:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-More_properly_an_effect_than_a_force?-2013-02-19T20:57:00.000Z&quot;,&quot;replies&quot;:[&quot;c-PaulTanenbaum-2013-02-19T20:57:00.000Z-More_properly_an_effect_than_a_force?&quot;],&quot;text&quot;:&quot;More properly an effect than a force?&quot;,&quot;linkableTitle&quot;:&quot;More properly an effect than a force?&quot;}--><h2 id="More_properly_an_effect_than_a_force?" data-mw-thread-id="h-More_properly_an_effect_than_a_force?-2013-02-19T20:57:00.000Z"><span id="More_properly_an_effect_than_a_force.3F"></span><span data-mw-comment-start="" id="h-More_properly_an_effect_than_a_force?-2013-02-19T20:57:00.000Z"></span>More properly an effect than a force?<span data-mw-comment-end="h-More_properly_an_effect_than_a_force?-2013-02-19T20:57:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Centrifugal_force_(rotating_reference_frame)&amp;action=edit&amp;section=2" title="Edit section: More properly an effect than a force?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><!--__DTELLIPSISBUTTON__{"threadItem":{"headingLevel":2,"name":"h-PaulTanenbaum-2013-02-19T20:57:00.000Z","type":"heading","level":0,"id":"h-More_properly_an_effect_than_a_force?-2013-02-19T20:57:00.000Z","replies":["c-PaulTanenbaum-2013-02-19T20:57:00.000Z-More_properly_an_effect_than_a_force?"]}}--><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"><!--__DTLATESTCOMMENTTHREAD__{"id":"c-Dicklyon-2013-02-20T05:49:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z","timestamp":"2013-02-20T05:49:00.000Z"}__--><!--__DTCOMMENTCOUNT__3__--><!--__DTAUTHORCOUNT__3__--></div><div class="ext-discussiontools-init-section-actions"><!--__DTSUBSCRIBEBUTTONMOBILE__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-PaulTanenbaum-2013-02-19T20:57:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-More_properly_an_effect_than_a_force?-2013-02-19T20:57:00.000Z&quot;,&quot;replies&quot;:[&quot;c-PaulTanenbaum-2013-02-19T20:57:00.000Z-More_properly_an_effect_than_a_force?&quot;],&quot;text&quot;:&quot;More properly an effect than a force?&quot;,&quot;linkableTitle&quot;:&quot;More properly an effect than a force?&quot;}--></div></div></div> <p><span data-mw-comment-start="" id="c-PaulTanenbaum-2013-02-19T20:57:00.000Z-More_properly_an_effect_than_a_force?"></span>I suspect that the lead would be better if reworked à la N.M.J. Woodhouse, who writes (p. 7) in his <i>Special Relativity</i> (Springer-Verlag, 2003), </p> <dl><dd>"In problems where the rotation matters, for example in the analysis of Foucault's pendulum, it is helpful to treat a terrestrial frame as if it were intertial, but to introduce correction terms, the 'fictitious' centrifugal and Coriolis forces, to take account of the rotation. But these are not real forces, and the frame is not really inertial."</dd></dl> <p>Indeed, even <a href="/wiki/Coriolis_effect" class="mw-redirect" title="Coriolis effect">Wikipedia's own article on Coriolis forces</a> is a redirect to <i>Coriolus effect</i>, and that article makes it clearer than this one does that the force is only apparent. I'd have just changed it myself, but wondered if there were a good argument for retaining the nonparallelism of treating one of the two forces as though it were somehow less fictitious than the other.—<a href="/wiki/User:PaulTanenbaum" title="User:PaulTanenbaum">PaulTanenbaum</a> (<a href="/wiki/User_talk:PaulTanenbaum" title="User talk:PaulTanenbaum">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Centrifugal_force_(rotating_reference_frame)#c-PaulTanenbaum-2013-02-19T20:57:00.000Z-More_properly_an_effect_than_a_force?" class="ext-discussiontools-init-timestamplink">20:57, 19 February 2013 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-PaulTanenbaum-2013-02-19T20:57:00.000Z-More_properly_an_effect_than_a_force?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2013-02-19T20:57:00.000Z","author":"PaulTanenbaum","type":"comment","level":1,"id":"c-PaulTanenbaum-2013-02-19T20:57:00.000Z-More_properly_an_effect_than_a_force?","replies":["c-FyzixFighter-2013-02-20T05:33:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z","c-Dicklyon-2013-02-20T05:49:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z"]}}--></span><span data-mw-comment-end="c-PaulTanenbaum-2013-02-19T20:57:00.000Z-More_properly_an_effect_than_a_force?"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-FyzixFighter-2013-02-20T05:33:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z"></span>My two cents here - I think there is a distinction between "effect" and "force" in these instances. My feeling from the literature that I've read is that the effect refers to the apparently anomalous deflection of the path of a particle while the force is the pseudo-force or fictitious force that is introduced to explain the deflection. As for an argument for retaining the nonparallelism, this is what we find in the literature, ie the terms "Coriolis effect" and "Coriolis force" are used with about the same frequency and sometimes it seems inter-changeably. The choice also seems to be dependent on the context - in meteorology we find "Coriolis effect" (and my guess this is true for the everyday person), while in the physics literature "Coriolis force" is more common. I don't think the same can be said for "centrifugal force"/"centrifugal effect". Just to get a general idea of how common the terms occur in the literature I searched for each phrase in google books: <ul><li>Coriolis effect : ~44,500</li> <li>Coriolis force : ~138,000</li> <li>Centrifugal effect : ~16,700</li> <li>Centrifugal force : ~1,260,000</li></ul></dd> <dd>That's almost two orders of magnitude difference for centrifugal between effect and force, while for Coriolis the two are roughly equal (okay, a factor of about 3 but less than an order of magnitude). So imo I don't care whether the other article is "Coriolis effect" or "Coriolis force", but I strongly favor keeping this one as "centrifugal force" per the usage frequency in the literature. That being said, if the intro needs to be clearer on it being a fictitious force then that should be fixed. --<a href="/wiki/User:FyzixFighter" title="User:FyzixFighter">FyzixFighter</a> (<a href="/wiki/User_talk:FyzixFighter" title="User talk:FyzixFighter">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Centrifugal_force_(rotating_reference_frame)#c-FyzixFighter-2013-02-20T05:33:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z" class="ext-discussiontools-init-timestamplink">05:33, 20 February 2013 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-FyzixFighter-2013-02-20T05:33:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2013-02-20T05:33:00.000Z","author":"FyzixFighter","type":"comment","level":2,"id":"c-FyzixFighter-2013-02-20T05:33:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z","replies":[]}}--></span><span data-mw-comment-end="c-FyzixFighter-2013-02-20T05:33:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z"></span></dd></dl> <dl><dd><span data-mw-comment-start="" id="c-Dicklyon-2013-02-20T05:49:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z"></span>I agree with FF. If you want it more parallel, go the other way. And I'd avoid the notion of "only apparent", since we already have a well-define notion of "fictitious force" that says exactly what it is. <a href="/wiki/User:Dicklyon" title="User:Dicklyon">Dicklyon</a> (<a href="/wiki/User_talk:Dicklyon" title="User talk:Dicklyon">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Centrifugal_force_(rotating_reference_frame)#c-Dicklyon-2013-02-20T05:49:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z" class="ext-discussiontools-init-timestamplink">05:49, 20 February 2013 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Dicklyon-2013-02-20T05:49:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2013-02-20T05:49:00.000Z","author":"Dicklyon","type":"comment","level":2,"id":"c-Dicklyon-2013-02-20T05:49:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z","replies":[]}}--></span><span data-mw-comment-end="c-Dicklyon-2013-02-20T05:49:00.000Z-PaulTanenbaum-2013-02-19T20:57:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><!--__DTSUBSCRIBEBUTTONDESKTOP__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-222.221.253.76-2013-03-06T02:13:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-Acceleration_Derivation-2013-03-06T02:13:00.000Z&quot;,&quot;replies&quot;:[&quot;c-222.221.253.76-2013-03-06T02:13:00.000Z-Acceleration_Derivation&quot;],&quot;text&quot;:&quot;Acceleration Derivation&quot;,&quot;linkableTitle&quot;:&quot;Acceleration Derivation&quot;}--><h2 id="Acceleration_Derivation" data-mw-thread-id="h-Acceleration_Derivation-2013-03-06T02:13:00.000Z"><span data-mw-comment-start="" id="h-Acceleration_Derivation-2013-03-06T02:13:00.000Z"></span>Acceleration Derivation<span data-mw-comment-end="h-Acceleration_Derivation-2013-03-06T02:13:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Centrifugal_force_(rotating_reference_frame)&amp;action=edit&amp;section=3" title="Edit section: Acceleration Derivation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><!--__DTELLIPSISBUTTON__{"threadItem":{"headingLevel":2,"name":"h-222.221.253.76-2013-03-06T02:13:00.000Z","type":"heading","level":0,"id":"h-Acceleration_Derivation-2013-03-06T02:13:00.000Z","replies":["c-222.221.253.76-2013-03-06T02:13:00.000Z-Acceleration_Derivation"]}}--><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"><!--__DTLATESTCOMMENTTHREAD__{"id":"c-DVdm-2013-03-06T12:47:00.000Z-222.221.253.76-2013-03-06T02:13:00.000Z","timestamp":"2013-03-06T12:47:00.000Z"}__--><!--__DTCOMMENTCOUNT__2__--><!--__DTAUTHORCOUNT__2__--></div><div class="ext-discussiontools-init-section-actions"><!--__DTSUBSCRIBEBUTTONMOBILE__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-222.221.253.76-2013-03-06T02:13:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-Acceleration_Derivation-2013-03-06T02:13:00.000Z&quot;,&quot;replies&quot;:[&quot;c-222.221.253.76-2013-03-06T02:13:00.000Z-Acceleration_Derivation&quot;],&quot;text&quot;:&quot;Acceleration Derivation&quot;,&quot;linkableTitle&quot;:&quot;Acceleration Derivation&quot;}--></div></div></div> <p><span data-mw-comment-start="" id="c-222.221.253.76-2013-03-06T02:13:00.000Z-Acceleration_Derivation"></span>In the derivation section, I'm noticing that the last two lines of equations in the "acceleration" section do not seem to follow from one another. When I evaluate the d/dt([dr/dt]+w x r) term in the next to last line, it does not give the factor of two in front of the Coriolis term. I believe the error is leaving out part of the first derivative operator: that is, in that equation, instead of the operator "d/dt" we should have "d/dt + w x" as the operator. (also see the rotational reference frame wiki page for that derivation, in which the derivation correctly gets the factor of two into the Coriolis term) I would just go ahead and add it, except I'm not at all familiar with the proper coding for inserting equations into wikipedia, and am very new here in general <span style="font-size: smaller;" class="autosigned">— Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/Special:Contributions/222.221.253.76" title="Special:Contributions/222.221.253.76">222.221.253.76</a> (<a href="/w/index.php?title=User_talk:222.221.253.76&amp;action=edit&amp;redlink=1" class="new" title="User talk:222.221.253.76 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Centrifugal_force_(rotating_reference_frame)#c-222.221.253.76-2013-03-06T02:13:00.000Z-Acceleration_Derivation" class="ext-discussiontools-init-timestamplink">02:13, 6 March 2013 (UTC)</a></span><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-222.221.253.76-2013-03-06T02:13:00.000Z-Acceleration_Derivation"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2013-03-06T02:13:00.000Z","author":"222.221.253.76","type":"comment","level":1,"id":"c-222.221.253.76-2013-03-06T02:13:00.000Z-Acceleration_Derivation","replies":["c-DVdm-2013-03-06T12:47:00.000Z-222.221.253.76-2013-03-06T02:13:00.000Z"]}}--></span><span data-mw-comment-end="c-222.221.253.76-2013-03-06T02:13:00.000Z-Acceleration_Derivation"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-DVdm-2013-03-06T12:47:00.000Z-222.221.253.76-2013-03-06T02:13:00.000Z"></span>It is correct. Don't forget that <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}=\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡<!-- ⁡ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡<!-- ⁡ --></mo> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡<!-- ⁡ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡<!-- ⁡ --></mo> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω<!-- ω --></mi> </mrow> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> <mtext> </mtext> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}=\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1efecc4293cca2e5e2f82e3bcb063f077a04d8a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.851ex; height:6.176ex;" alt="{\displaystyle {\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}=\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ ,}"/></span></dd></dl></dd> <dd>and of course likewise <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\operatorname {d} }{\operatorname {d} t}}\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]=\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]\ ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">d</mi> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡<!-- ⁡ --></mo> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡<!-- ⁡ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡<!-- ⁡ --></mo> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> <mo>=</mo> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡<!-- ⁡ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡<!-- ⁡ --></mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">ω<!-- ω --></mi> </mrow> <mo>×<!-- × --></mo> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡<!-- ⁡ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold-italic">r</mi> </mrow> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡<!-- ⁡ --></mo> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> <mtext> </mtext> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\operatorname {d} }{\operatorname {d} t}}\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]=\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]\ ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4759fa2bad1a1e430e18b7280b642703738d1b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:35.461ex; height:6.343ex;" alt="{\displaystyle {\frac {\operatorname {d} }{\operatorname {d} t}}\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]=\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]\ ,}"/></span></dd></dl></dd> <dd>so that is where the second term comes from.</dd> <dd><b>Note</b> - this derivation could need a source. - <a href="/wiki/User:DVdm" title="User:DVdm">DVdm</a> (<a href="/wiki/User_talk:DVdm" title="User talk:DVdm">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Centrifugal_force_(rotating_reference_frame)#c-DVdm-2013-03-06T12:47:00.000Z-222.221.253.76-2013-03-06T02:13:00.000Z" class="ext-discussiontools-init-timestamplink">12:47, 6 March 2013 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-DVdm-2013-03-06T12:47:00.000Z-222.221.253.76-2013-03-06T02:13:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2013-03-06T12:47:00.000Z","author":"DVdm","type":"comment","level":2,"id":"c-DVdm-2013-03-06T12:47:00.000Z-222.221.253.76-2013-03-06T02:13:00.000Z","replies":[]}}--></span><span data-mw-comment-end="c-DVdm-2013-03-06T12:47:00.000Z-222.221.253.76-2013-03-06T02:13:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><!--__DTSUBSCRIBEBUTTONDESKTOP__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-Montyv-2015-05-31T17:32:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t-2015-05-31T17:32:00.000Z&quot;,&quot;replies&quot;:[&quot;c-Montyv-2015-05-31T17:32:00.000Z-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t&quot;],&quot;text&quot;:&quot;It's the rotation of the direction of the velocity vector that matters, not of the frame.&quot;,&quot;linkableTitle&quot;:&quot;It's the rotation of the direction of the velocity vector that matters, not of the frame.&quot;}--><h2 id="It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_the_frame." data-mw-thread-id="h-It&#039;s_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t-2015-05-31T17:32:00.000Z"><span id="It.27s_the_rotation_of_the_direction_of_the_velocity_vector_that_matters.2C_not_of_the_frame."></span><span data-mw-comment-start="" id="h-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t-2015-05-31T17:32:00.000Z"></span>It's the rotation of the <i>direction of the velocity vector</i> that matters, not of the frame.<span data-mw-comment-end="h-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t-2015-05-31T17:32:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Centrifugal_force_(rotating_reference_frame)&amp;action=edit&amp;section=4" title="Edit section: It&#039;s the rotation of the direction of the velocity vector that matters, not of the frame."><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><!--__DTELLIPSISBUTTON__{"threadItem":{"headingLevel":2,"name":"h-Montyv-2015-05-31T17:32:00.000Z","type":"heading","level":0,"id":"h-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t-2015-05-31T17:32:00.000Z","replies":["c-Montyv-2015-05-31T17:32:00.000Z-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t"]}}--><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"><!--__DTLATESTCOMMENTTHREAD__{"id":"c-Montyv-2015-05-31T17:32:00.000Z-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t","timestamp":"2015-05-31T17:32:00.000Z"}__--><!--__DTCOMMENTCOUNT__1__--><!--__DTAUTHORCOUNT__1__--></div><div class="ext-discussiontools-init-section-actions"><!--__DTSUBSCRIBEBUTTONMOBILE__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-Montyv-2015-05-31T17:32:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t-2015-05-31T17:32:00.000Z&quot;,&quot;replies&quot;:[&quot;c-Montyv-2015-05-31T17:32:00.000Z-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t&quot;],&quot;text&quot;:&quot;It's the rotation of the direction of the velocity vector that matters, not of the frame.&quot;,&quot;linkableTitle&quot;:&quot;It's the rotation of the direction of the velocity vector that matters, not of the frame.&quot;}--></div></div></div> <p><span data-mw-comment-start="" id="c-Montyv-2015-05-31T17:32:00.000Z-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t"></span>Yep. We have here a misleading article title, and misleading wording that implies that a <i>reference frame'</i>s rotation results in centrifugal force/pseudoforce. Rather, it's the <i>centripetal acceleration</i> of the frame (or object) that results in such forces. The centripetal acceleration of the frame (stated in an inertial frame) is proportional to the rate of change of the <i>direction of the velocity vector</i> (also stated in the same inertial frame). Thus, if the rate of rotation of anything matters, it's the rate of rotation of the direction of the velocity vector, <i>not</i> the rotation rate of the frame. </p><p>I grant that, in most usual cases (such as ball-on-string), the most common frame is attached to the object (ball) and is also rotating along with the object. The rotation rate of the frame in these cases is the same as the rotation rate of the direction of the velocity vector, <i>but that's only incidental</i>. It's the rate of change of the direction of the velocity vector that makes for the centrifugal forces here. If the frame was still attached to the ball, but was chosen to rotate at twice or three times the rate of the velocity vector, or if it was chosen to not rotate at all, it would not effect the magnitude of the centrifugal force, nor would it effect the actual direction of the centrifugal force. Such an independently-rotating frame would have different <i>numbers</i> representing the direction of the centrifugal force, but the actual direction (or magnitude) of the centrifugal force at any particular moment would not vary with rotation rate of the frame. </p><p>We should not muddle-together the <i>movement</i> of a frame (such as in a circle about a point) with <i>rotation</i> of the frame. They are two different things that can be independent. If we don't keep that in mind, it leads to fallacies. </p><p><a href="/wiki/User:Montyv" title="User:Montyv">Montyv</a> (<a href="/wiki/User_talk:Montyv" title="User talk:Montyv">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Centrifugal_force_(rotating_reference_frame)#c-Montyv-2015-05-31T17:32:00.000Z-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t" class="ext-discussiontools-init-timestamplink">17:32, 31 May 2015 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Montyv-2015-05-31T17:32:00.000Z-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2015-05-31T17:32:00.000Z","author":"Montyv","type":"comment","level":1,"id":"c-Montyv-2015-05-31T17:32:00.000Z-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t","replies":[]}}--></span><span data-mw-comment-end="c-Montyv-2015-05-31T17:32:00.000Z-It's_the_rotation_of_the_direction_of_the_velocity_vector_that_matters,_not_of_t"></span> </p> <!-- NewPP limit report Parsed by mw‐web.codfw.main‐759d5489db‐vc5kz Cached time: 20241202184825 Cache expiry: 864000 Reduced expiry: true Complications: [vary‐revision‐sha1, show‐toc] DiscussionTools time usage: 0.019 seconds CPU time usage: 0.336 seconds Real time usage: 0.467 seconds Preprocessor visited node count: 1388/1000000 Post‐expand include size: 55233/2097152 bytes Template argument size: 1353/2097152 bytes Highest expansion depth: 16/100 Expensive parser function count: 31/500 Unstrip recursion depth: 0/20 Unstrip post‐expand size: 30335/5000000 bytes Lua time usage: 0.162/10.000 seconds Lua memory usage: 3374446/52428800 bytes Number of Wikibase entities loaded: 0/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 338.356 1 -total 38.00% 128.590 1 Template:WikiProject_banner_shell 28.37% 95.985 1 Template:Archives 26.87% 90.918 1 Template:Talk_header 19.51% 66.016 1 Template:WikiProject_Physics 17.16% 58.053 11 Template:Th/abp 8.25% 27.910 1 Template:Find_sources 7.87% 26.642 9 Template:Tmpv 5.91% 20.012 2 Template:Pagetype 5.85% 19.798 11 Template:HasTemplate --> <!-- Saved in parser cache with key enwiki:pcache:7533:|#|:idhash:canonical and timestamp 20241202184825 and revision id 1259523219. 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