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Treghetsmoment – Wikipedia
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class="mf-section-0" id="mf-section-0"> <style data-mw-deduplicate="TemplateStyles:r24553676">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}</style> <table class="plainlinks metadata ambox ambox-content ambox-Unsourced" role="presentation"> <tbody> <tr> <td class="mbox-text"> <div class="mbox-text-span"> <b>Kildeløs</b>: Denne artikkelen mangler <a href="https://no-m-wikipedia-org.translate.goog/wiki/Wikipedia:Bruk_av_kilder?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wikipedia:Bruk av kilder">kildehenvisninger</a>, og opplysningene i den kan dermed være vanskelige å <a href="https://no-m-wikipedia-org.translate.goog/wiki/Wikipedia:Verifiserbarhet?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wikipedia:Verifiserbarhet">verifisere</a>. Kildeløst materiale kan bli <a href="https://no-m-wikipedia-org.translate.goog/wiki/Wikipedia:Verifiserbarhet?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Bevisbyrden" title="Wikipedia:Verifiserbarhet">fjernet</a>. Helt uten kilder. <span class="date-container"><i>(<span class="date">7. januar 2017</span>)</i></span> </div></td> </tr> </tbody> </table> <p><br></p> <dl> <dd> <i>Denne artikkelen omhandler momentet for et roterende legeme. Se <a href="https://no-m-wikipedia-org.translate.goog/wiki/Annet_arealmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Annet arealmoment">Annet arealmoment</a> for momentet til et bøyd plan.</i> </dd> </dl> <p><b>Treghetsmomentet</b> (<a href="https://no-m-wikipedia-org.translate.goog/wiki/SI-systemet?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="SI-systemet">SI</a>-enhet kg·m<sup>2</sup>) er et mål på rotasjonstregheten til et stivt legeme. Symbolet <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 I}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I} </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> brukes vanligvis for å referere til <i>treghetsmomentet</i>.</p> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"> <input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"> <div class="toctitle" lang="nb" dir="ltr"> <h2 id="mw-toc-heading">Innhold</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span> </div> <ul> <li class="toclevel-1 tocsection-1"><a href="https://no-m-wikipedia-org.translate.goog/wiki/Treghetsmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Oversikt"><span class="tocnumber">1</span> <span class="toctext">Oversikt</span></a></li> <li class="toclevel-1 tocsection-2"><a href="https://no-m-wikipedia-org.translate.goog/wiki/Treghetsmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Skalart_treghetsmoment"><span class="tocnumber">2</span> <span class="toctext">Skalart treghetsmoment</span></a> <ul> <li class="toclevel-2 tocsection-3"><a href="https://no-m-wikipedia-org.translate.goog/wiki/Treghetsmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Definisjon"><span class="tocnumber">2.1</span> <span class="toctext">Definisjon</span></a></li> <li class="toclevel-2 tocsection-4"><a href="https://no-m-wikipedia-org.translate.goog/wiki/Treghetsmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Parallellakseteoremet"><span class="tocnumber">2.2</span> <span class="toctext">Parallellakseteoremet</span></a> <ul> <li class="toclevel-3 tocsection-5"><a href="https://no-m-wikipedia-org.translate.goog/wiki/Treghetsmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Et_utvalg_kjente_treghetsmomenter"><span class="tocnumber">2.2.1</span> <span class="toctext">Et utvalg kjente treghetsmomenter</span></a></li> </ul></li> <li class="toclevel-2 tocsection-6"><a href="https://no-m-wikipedia-org.translate.goog/wiki/Treghetsmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Kinetisk_energi"><span class="tocnumber">2.3</span> <span class="toctext">Kinetisk energi</span></a></li> </ul></li> </ul> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Oversikt">Oversikt</h2><span class="mw-editsection"> <a role="button" href="https://no-m-wikipedia-org.translate.goog/w/index.php?title=Treghetsmoment&action=edit&section=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Rediger avsnitt: Oversikt" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>rediger</span> </a> </span> </div> <section class="mf-section-1 collapsible-block" id="mf-section-1"> <p>Et legemes treghetsmoment om en gitt akse beskriver hvor vanskelig det er å sette legemet i rotasjon om aksen, der aksen går gjennom legemets <a href="https://no-m-wikipedia-org.translate.goog/wiki/Massefellespunkt?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Massefellespunkt">massefellespunkt</a>. Som et eksempel, tenk på to hjul med samme masse, et med stor og et med liten radius. Det mindre hjulet er lettere å akselerere inn i en rotasjonsbevegelse, fordi at massen er konsentrert nærmere rotasjonsaksen. Tilsvarende er det vanskeligere å få det større hjulet til å akselerere, siden massen er spredt lenger fra rotasjonsaksen. Det lille hjulet har et mindre treghetsmoment, mens det større hjulet har et større treghetsmoment.</p> <p>Treghetsmomentet må ikke forveksles med <a href="https://no-m-wikipedia-org.translate.goog/wiki/Annet_arealmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Annet arealmoment">annet arealmoment</a> eller <a href="https://no-m-wikipedia-org.translate.goog/w/index.php?title=Polart_arealmoment&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="new" title="Polart arealmoment (ikke skrevet ennå)">polart arealmoment</a>, som ofte har samme symbol <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 I}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"> </noscript><span class="lazy-image-placeholder" style="width: 1.172ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" data-alt="{\displaystyle I}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>.</p> <p>Det finnes to former av treghetsmoment; en skalar form, og en mer generell form, der det ikke er nødvendig å vite rotasjonsaksen. Det skalare treghetsmomentet er ofte det man refererer til og forstår med "treghetsmoment", og den generelle formen omtales derfor ikke i denne artikkelen.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Skalart_treghetsmoment">Skalart treghetsmoment</h2><span class="mw-editsection"> <a role="button" href="https://no-m-wikipedia-org.translate.goog/w/index.php?title=Treghetsmoment&action=edit&section=2&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Rediger avsnitt: Skalart treghetsmoment" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>rediger</span> </a> </span> </div> <section class="mf-section-2 collapsible-block" id="mf-section-2"> <div class="mw-heading mw-heading3"> <h3 id="Definisjon">Definisjon</h3><span class="mw-editsection"> <a role="button" href="https://no-m-wikipedia-org.translate.goog/w/index.php?title=Treghetsmoment&action=edit&section=3&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Rediger avsnitt: Definisjon" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>rediger</span> </a> </span> </div> <p>Det (skalare) treghetsmomentet for et massepunkt som roterer om en kjent akse er:</p> <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 I\ {\stackrel {\mathrm {def} }{=}}\ mr^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo> = </mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> d </mi> <mi mathvariant="normal"> e </mi> <mi mathvariant="normal"> f </mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <mi> m </mi> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I\ {\stackrel {\mathrm {def} }{=}}\ mr^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61b66ef44c7ae91a775258782f01855c343debb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.387ex; width:9.119ex; height:3.343ex;" alt="{\displaystyle I\ {\stackrel {\mathrm {def} }{=}}\ mr^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 9.119ex;height: 3.343ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61b66ef44c7ae91a775258782f01855c343debb8" data-alt="{\displaystyle I\ {\stackrel {\mathrm {def} }{=}}\ mr^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>der</p> <dl> <dd> <i>m</i> er massen, </dd> <dd> og <i>r</i> er avstand fra massepunktet til rotasjonsaksen. </dd> </dl> <p>Treghetsmomentet kan summeres, så for et legeme definert som flere massepunkt med masse <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 m_{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle m_{i}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ec8e804f69706d3f5ad235f4f983220c8df7c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.84ex; height:2.009ex;" alt="{\displaystyle m_{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 2.84ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ec8e804f69706d3f5ad235f4f983220c8df7c2" data-alt="{\displaystyle m_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> og avstand fra rotasjonsaksen <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 r_{i}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r_{i}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0b6d651eaf432dbf1f106021c8bb499ae83fd1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.848ex; height:2.009ex;" alt="{\displaystyle r_{i}}"> </noscript><span class="lazy-image-placeholder" style="width: 1.848ex;height: 2.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0b6d651eaf432dbf1f106021c8bb499ae83fd1f" data-alt="{\displaystyle r_{i}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>, er det totale treghetsmomentet summen av treghetsmomentene for hver enkelt massepunkt.</p> <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 I\ {\stackrel {\mathrm {def} }{=}}\ \sum _{i=1}^{N}{m_{i}r_{i}^{2}}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo> = </mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> d </mi> <mi mathvariant="normal"> e </mi> <mi mathvariant="normal"> f </mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <munderover> <mo> ∑<!-- ∑ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> N </mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> </mrow> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I\ {\stackrel {\mathrm {def} }{=}}\ \sum _{i=1}^{N}{m_{i}r_{i}^{2}}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c74f382526b23db1c57c3e3af3ce700a1da2e7da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-right: -0.387ex; width:14.048ex; height:7.343ex;" alt="{\displaystyle I\ {\stackrel {\mathrm {def} }{=}}\ \sum _{i=1}^{N}{m_{i}r_{i}^{2}}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 14.048ex;height: 7.343ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c74f382526b23db1c57c3e3af3ce700a1da2e7da" data-alt="{\displaystyle I\ {\stackrel {\mathrm {def} }{=}}\ \sum _{i=1}^{N}{m_{i}r_{i}^{2}}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>For en kontinuerlig massefordeling er treghetsmomentet definert ved uttrykket</p> <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 I\ {\stackrel {\mathrm {def} }{=}}\ \ \int r^{2}dm}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo> = </mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> d </mi> <mi mathvariant="normal"> e </mi> <mi mathvariant="normal"> f </mi> </mrow> </mrow> </mover> </mrow> </mrow> <mtext> </mtext> <mtext> </mtext> <mo> ∫<!-- ∫ --> </mo> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mi> d </mi> <mi> m </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I\ {\stackrel {\mathrm {def} }{=}}\ \ \int r^{2}dm} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be76af4a61cd5085541996f1c2c8319aa33e2a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:13.496ex; height:5.676ex;" alt="{\displaystyle I\ {\stackrel {\mathrm {def} }{=}}\ \ \int r^{2}dm}"> </noscript><span class="lazy-image-placeholder" style="width: 13.496ex;height: 5.676ex;vertical-align: -2.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be76af4a61cd5085541996f1c2c8319aa33e2a6" data-alt="{\displaystyle I\ {\stackrel {\mathrm {def} }{=}}\ \ \int r^{2}dm}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <div class="mw-heading mw-heading3"> <h3 id="Parallellakseteoremet"><a href="https://no-m-wikipedia-org.translate.goog/wiki/Parallellakseteoremet?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Parallellakseteoremet">Parallellakseteoremet</a></h3><span class="mw-editsection"> <a role="button" href="https://no-m-wikipedia-org.translate.goog/w/index.php?title=Treghetsmoment&action=edit&section=4&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Rediger avsnitt: Parallellakseteoremet" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>rediger</span> </a> </span> </div> <p>Hvis treghetsmomentet for rotasjon om en akse gjennom massefellespunktet for et symmetrisk legeme har blitt kalkulert, kan man finne treghetsmomentet for rotasjon om alle parallelle akser. For en rotasjonsakse en avstand <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 R}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> R </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle R} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"> </noscript><span class="lazy-image-placeholder" style="width: 1.764ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" data-alt="{\displaystyle R}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> fra massefellespunktet, blir det nye treghetsmomentet:</p> <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 I_{\mathrm {nyakse} }=I_{\mathrm {massefellespunkt} }+MR^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> n </mi> <mi mathvariant="normal"> y </mi> <mi mathvariant="normal"> a </mi> <mi mathvariant="normal"> k </mi> <mi mathvariant="normal"> s </mi> <mi mathvariant="normal"> e </mi> </mrow> </mrow> </msub> <mo> = </mo> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> m </mi> <mi mathvariant="normal"> a </mi> <mi mathvariant="normal"> s </mi> <mi mathvariant="normal"> s </mi> <mi mathvariant="normal"> e </mi> <mi mathvariant="normal"> f </mi> <mi mathvariant="normal"> e </mi> <mi mathvariant="normal"> l </mi> <mi mathvariant="normal"> l </mi> <mi mathvariant="normal"> e </mi> <mi mathvariant="normal"> s </mi> <mi mathvariant="normal"> p </mi> <mi mathvariant="normal"> u </mi> <mi mathvariant="normal"> n </mi> <mi mathvariant="normal"> k </mi> <mi mathvariant="normal"> t </mi> </mrow> </mrow> </msub> <mo> + </mo> <mi> M </mi> <msup> <mi> R </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {nyakse} }=I_{\mathrm {massefellespunkt} }+MR^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/842dd1baac10d13d0ec4168c06e8deafe25d817d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:31.047ex; height:3.343ex;" alt="{\displaystyle I_{\mathrm {nyakse} }=I_{\mathrm {massefellespunkt} }+MR^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 31.047ex;height: 3.343ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/842dd1baac10d13d0ec4168c06e8deafe25d817d" data-alt="{\displaystyle I_{\mathrm {nyakse} }=I_{\mathrm {massefellespunkt} }+MR^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>der</p> <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 M}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> M </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle M} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"> </noscript><span class="lazy-image-placeholder" style="width: 2.442ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" data-alt="{\displaystyle M}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> er legemets totale masse, </dd> <dd> og <i>R</i> er avstanden fra den nye rotasjonsaksen til massefellespunktet. </dd> </dl> <p>Dette teoremet er også kjent som Steiners sats.</p> <p>Et eksempel på bruk av denne formelen vil være hvis man i stedet for å rotere et hjul rundt akselen, spinner det rundt en ny aksel helt i ytterkanten av hjulet. Det nye treghetsmomentet vil bli det opprinnelige treghetsmomentet pluss massen til hjulet ganget med hjulradiusen i andre.</p> <div class="mw-heading mw-heading4"> <h4 id="Et_utvalg_kjente_treghetsmomenter">Et utvalg kjente treghetsmomenter</h4><span class="mw-editsection"> <a role="button" href="https://no-m-wikipedia-org.translate.goog/w/index.php?title=Treghetsmoment&action=edit&section=5&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Rediger avsnitt: Et utvalg kjente treghetsmomenter" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>rediger</span> </a> </span> </div> <p>Dette er kjente treghetsmomenter for en del vanlige geometriske former med rotasjonsakse gjennom massefellespunktet. Disse kan benyttes for <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 I_{\mathrm {massefellespunkt} }\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> m </mi> <mi mathvariant="normal"> a </mi> <mi mathvariant="normal"> s </mi> <mi mathvariant="normal"> s </mi> <mi mathvariant="normal"> e </mi> <mi mathvariant="normal"> f </mi> <mi mathvariant="normal"> e </mi> <mi mathvariant="normal"> l </mi> <mi mathvariant="normal"> l </mi> <mi mathvariant="normal"> e </mi> <mi mathvariant="normal"> s </mi> <mi mathvariant="normal"> p </mi> <mi mathvariant="normal"> u </mi> <mi mathvariant="normal"> n </mi> <mi mathvariant="normal"> k </mi> <mi mathvariant="normal"> t </mi> </mrow> </mrow> </msub> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {massefellespunkt} }\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca11e6b3abf85841c0be4b86dc84f9fae6c744e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-right: -0.387ex; width:13.743ex; height:2.843ex;" alt="{\displaystyle I_{\mathrm {massefellespunkt} }\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 13.743ex;height: 2.843ex;vertical-align: -1.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca11e6b3abf85841c0be4b86dc84f9fae6c744e2" data-alt="{\displaystyle I_{\mathrm {massefellespunkt} }\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> i parallellakseteoremet. Alle former har masse M.</p> <p><br><b>Homogen slank stav</b> med lengde <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 L}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> L </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle L} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"> </noscript><span class="lazy-image-placeholder" style="width: 1.583ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" data-alt="{\displaystyle L}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> langs y-aksen:</p> <p><br></p> <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 I_{\mathrm {z} }=I_{\mathrm {x} }={\frac {1}{12}}ML^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> z </mi> </mrow> </mrow> </msub> <mo> = </mo> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> x </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mrow> <mi> M </mi> <msup> <mi> L </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {z} }=I_{\mathrm {x} }={\frac {1}{12}}ML^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89dcfea238dfb4a495f296501d248fe5fbb1aad2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:18.933ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {z} }=I_{\mathrm {x} }={\frac {1}{12}}ML^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 18.933ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89dcfea238dfb4a495f296501d248fe5fbb1aad2" data-alt="{\displaystyle I_{\mathrm {z} }=I_{\mathrm {x} }={\frac {1}{12}}ML^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p><br><b>Tynn rektangulær plate</b> i xy-planet med sidekant <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 a}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> a </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle a} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"> </noscript><span class="lazy-image-placeholder" style="width: 1.23ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" data-alt="{\displaystyle a}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> langs x-aksen og sidekant <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 b}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> b </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle b} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"> </noscript><span class="lazy-image-placeholder" style="width: 0.998ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" data-alt="{\displaystyle b}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> langs y-aksen.</p> <p><br></p> <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 I_{\mathrm {z} }={\frac {1}{12}}M(a^{2}+b^{2})\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> z </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mrow> <mi> M </mi> <mo stretchy="false"> ( </mo> <msup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <msup> <mi> b </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo stretchy="false"> ) </mo> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {z} }={\frac {1}{12}}M(a^{2}+b^{2})\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1dfd733ebc5c06d757e8158cd4284762f0e756e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:20.06ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {z} }={\frac {1}{12}}M(a^{2}+b^{2})\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 20.06ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1dfd733ebc5c06d757e8158cd4284762f0e756e" data-alt="{\displaystyle I_{\mathrm {z} }={\frac {1}{12}}M(a^{2}+b^{2})\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <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 I_{\mathrm {x} }={\frac {1}{12}}Mb^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> x </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mrow> <mi> M </mi> <msup> <mi> b </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {x} }={\frac {1}{12}}Mb^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b57d82274c344e51d81c1e994083308fc412c1bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:13.264ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {x} }={\frac {1}{12}}Mb^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 13.264ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b57d82274c344e51d81c1e994083308fc412c1bc" data-alt="{\displaystyle I_{\mathrm {x} }={\frac {1}{12}}Mb^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <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 I_{\mathrm {y} }={\frac {1}{12}}Ma^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> y </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mrow> <mi> M </mi> <msup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {y} }={\frac {1}{12}}Ma^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d28ff40c167e3dfc5c630db4be7fb8ea09fd841e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:13.496ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {y} }={\frac {1}{12}}Ma^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 13.496ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d28ff40c167e3dfc5c630db4be7fb8ea09fd841e" data-alt="{\displaystyle I_{\mathrm {y} }={\frac {1}{12}}Ma^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p><br><b>Rektangulært prisme</b> med sidekant b langs y-aksen og sidekant a langs x-aksen, med vilkårlig høyde langs z-aksen.</p> <p><br></p> <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 I_{\mathrm {z} }={\frac {1}{12}}M(a^{2}+b^{2})\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> z </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mrow> <mi> M </mi> <mo stretchy="false"> ( </mo> <msup> <mi> a </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <msup> <mi> b </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo stretchy="false"> ) </mo> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {z} }={\frac {1}{12}}M(a^{2}+b^{2})\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1dfd733ebc5c06d757e8158cd4284762f0e756e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:20.06ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {z} }={\frac {1}{12}}M(a^{2}+b^{2})\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 20.06ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1dfd733ebc5c06d757e8158cd4284762f0e756e" data-alt="{\displaystyle I_{\mathrm {z} }={\frac {1}{12}}M(a^{2}+b^{2})\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p><br><b>Tynn sirkulær skive</b> med radius r i xy-planet.</p> <p><br></p> <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 I_{\mathrm {z} }={\frac {1}{2}}Mr^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> z </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mi> M </mi> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {z} }={\frac {1}{2}}Mr^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b2cfd8916552e1e199c69bd7851d1d9dcee9051" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:12.015ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {z} }={\frac {1}{2}}Mr^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 12.015ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b2cfd8916552e1e199c69bd7851d1d9dcee9051" data-alt="{\displaystyle I_{\mathrm {z} }={\frac {1}{2}}Mr^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <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 I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{4}}Mr^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> x </mi> </mrow> </mrow> </msub> <mo> = </mo> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> y </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> <mi> M </mi> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{4}}Mr^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb31dd12849b3bfc0922c9ac9f2f87065c6373ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:17.374ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{4}}Mr^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 17.374ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb31dd12849b3bfc0922c9ac9f2f87065c6373ae" data-alt="{\displaystyle I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{4}}Mr^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p><br><b>Sirkulær sylinder</b> langs z-aksen med radius r og lengde L.</p> <p><br></p> <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 I_{\mathrm {z} }={\frac {1}{2}}Mr^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> z </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mi> M </mi> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {z} }={\frac {1}{2}}Mr^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b2cfd8916552e1e199c69bd7851d1d9dcee9051" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:12.015ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {z} }={\frac {1}{2}}Mr^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 12.015ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b2cfd8916552e1e199c69bd7851d1d9dcee9051" data-alt="{\displaystyle I_{\mathrm {z} }={\frac {1}{2}}Mr^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <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 I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{12}}M(3r^{2}+L^{2})\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> x </mi> </mrow> </mrow> </msub> <mo> = </mo> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> y </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mrow> <mi> M </mi> <mo stretchy="false"> ( </mo> <mn> 3 </mn> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <msup> <mi> L </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo stretchy="false"> ) </mo> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{12}}M(3r^{2}+L^{2})\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f93b247a47710750d5549e0737afae07d2f64b05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:26.986ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{12}}M(3r^{2}+L^{2})\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 26.986ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f93b247a47710750d5549e0737afae07d2f64b05" data-alt="{\displaystyle I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{12}}M(3r^{2}+L^{2})\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p><br><b>Tynt sylinderskall</b> langs z-aksen med radius r og lengde L:</p> <p><br></p> <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 I_{\mathrm {z} }=Mr^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> z </mi> </mrow> </mrow> </msub> <mo> = </mo> <mi> M </mi> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {z} }=Mr^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/260dd7797c4db73ab9f486b15fa9712bca35249d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:10.016ex; height:3.009ex;" alt="{\displaystyle I_{\mathrm {z} }=Mr^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 10.016ex;height: 3.009ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/260dd7797c4db73ab9f486b15fa9712bca35249d" data-alt="{\displaystyle I_{\mathrm {z} }=Mr^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <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 I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{2}}Mr^{2}+{\frac {1}{12}}ML^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> x </mi> </mrow> </mrow> </msub> <mo> = </mo> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> y </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mi> M </mi> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mrow> <mi> M </mi> <msup> <mi> L </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{2}}Mr^{2}+{\frac {1}{12}}ML^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e82882c4ef764500a07626c50c9df562b822d438" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:28.455ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{2}}Mr^{2}+{\frac {1}{12}}ML^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 28.455ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e82882c4ef764500a07626c50c9df562b822d438" data-alt="{\displaystyle I_{\mathrm {x} }=I_{\mathrm {y} }={\frac {1}{2}}Mr^{2}+{\frac {1}{12}}ML^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p><br><b>Kule</b> med radius r har samme treghetsmoment om alle akser gjennom massefellespunktet:</p> <p><br></p> <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 I_{\mathrm {} }={\frac {2}{5}}Mr^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 2 </mn> <mn> 5 </mn> </mfrac> </mrow> <mi> M </mi> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {} }={\frac {2}{5}}Mr^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8de53840dc2cbfa4beae804cc21b2d4bc05fe49e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:11.201ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {} }={\frac {2}{5}}Mr^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 11.201ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8de53840dc2cbfa4beae804cc21b2d4bc05fe49e" data-alt="{\displaystyle I_{\mathrm {} }={\frac {2}{5}}Mr^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p><br><b>Kuleskall</b> med raduis r har også samme treghetsmoment om alle akser gjennom massefellespunktet:</p> <p><br></p> <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 I_{\mathrm {} }={\frac {2}{3}}Mr^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> <mi> M </mi> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {} }={\frac {2}{3}}Mr^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a99384c335427960dd104d49d93f130be15901d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:11.201ex; height:5.176ex;" alt="{\displaystyle I_{\mathrm {} }={\frac {2}{3}}Mr^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 11.201ex;height: 5.176ex;vertical-align: -1.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a99384c335427960dd104d49d93f130be15901d0" data-alt="{\displaystyle I_{\mathrm {} }={\frac {2}{3}}Mr^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <div class="mw-heading mw-heading3"> <h3 id="Kinetisk_energi">Kinetisk energi</h3><span class="mw-editsection"> <a role="button" href="https://no-m-wikipedia-org.translate.goog/w/index.php?title=Treghetsmoment&action=edit&section=6&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Rediger avsnitt: Kinetisk energi" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>rediger</span> </a> </span> </div> <p>For et legeme som roterer med konstant vinkelhastighet <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 \omega }"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> ω<!-- ω --> </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \omega } </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"> </noscript><span class="lazy-image-placeholder" style="width: 1.446ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" data-alt="{\displaystyle \omega }" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> om en akse, er den kinetiske rotasjonsenergien <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 T}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> T </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle T} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"> </noscript><span class="lazy-image-placeholder" style="width: 1.636ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" data-alt="{\displaystyle T}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> gitt ved:</p> <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 T=\sum _{i=1}^{N}{\frac {1}{2}}m_{i}\omega ^{2}r_{i}^{2}={\frac {1}{2}}I\omega ^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> T </mi> <mo> = </mo> <munderover> <mo> ∑<!-- ∑ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi> N </mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <msub> <mi> m </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </msub> <msup> <mi> ω<!-- ω --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mi> I </mi> <msup> <mi> ω<!-- ω --> </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mspace width="negativethinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle T=\sum _{i=1}^{N}{\frac {1}{2}}m_{i}\omega ^{2}r_{i}^{2}={\frac {1}{2}}I\omega ^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e54929ed658c94a5e9d86e477986c3e36a1d413f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; margin-right: -0.387ex; width:27.074ex; height:7.343ex;" alt="{\displaystyle T=\sum _{i=1}^{N}{\frac {1}{2}}m_{i}\omega ^{2}r_{i}^{2}={\frac {1}{2}}I\omega ^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 27.074ex;height: 7.343ex;vertical-align: -3.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e54929ed658c94a5e9d86e477986c3e36a1d413f" data-alt="{\displaystyle T=\sum _{i=1}^{N}{\frac {1}{2}}m_{i}\omega ^{2}r_{i}^{2}={\frac {1}{2}}I\omega ^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> </dd> </dl> <p>Formelen holder også for rulling av hjul.</p> <style data-mw-deduplicate="TemplateStyles:r24790658">.mw-parser-output .spire{clear:both;border:1px solid var(--border-color-base,#a2a9b1);border-radius:2px;padding:0.325rem;padding-left:3rem;margin:0.5rem 0;font-size:0.8125rem;background-color:var(--background-color-neutral-subtle,#f8f9fa);background-image:url("https://upload.wikimedia.org/wikipedia/commons/2/2d/Stub_W.svg"),url("https://upload.wikimedia.org/wikipedia/commons/c/ce/Emojione_1F331.svg"),url("https://upload.wikimedia.org/wikipedia/commons/7/7a/Grass_compartment.svg");background-repeat:no-repeat;background-position:0.5rem center,bottom right 0.5rem,bottom -2.1rem right -4rem;background-size:2rem,1.8rem,10rem;padding-right:3rem;text-align:start}</style> <div class="spire plainlinks"> Denne artikkelen er en <b><a href="https://no-m-wikipedia-org.translate.goog/wiki/Wikipedia:Spire?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wikipedia:Spire">spire</a></b>. 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Rendering was triggered because: page-view --> </section> </div><!-- MobileFormatter took 0.013 seconds --><!--esi <esi:include src="/esitest-fa8a495983347898/content" /> --> <noscript> <img src="https://login.m.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&mobile=1" alt="" width="1" height="1" style="border: none; position: absolute;"> </noscript> <div class="printfooter" data-nosnippet=""> Hentet fra «<a dir="ltr" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://no.wikipedia.org/w/index.php?title%3DTreghetsmoment%26oldid%3D23988444">https://no.wikipedia.org/w/index.php?title=Treghetsmoment&oldid=23988444</a>» </div> </div> </div> <div class="post-content" id="page-secondary-actions"> </div> </main> <footer class="mw-footer minerva-footer" role="contentinfo"><a class="last-modified-bar" href="https://no-m-wikipedia-org.translate.goog/w/index.php?title=Treghetsmoment&action=history&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB"> <div class="post-content last-modified-bar__content"><span class="minerva-icon minerva-icon-size-medium minerva-icon--modified-history"></span> <span class="last-modified-bar__text modified-enhancement" data-user-name="JhsBot" data-user-gender="unknown" data-timestamp="1700675651"> <span>Sist redigert 22. nov. 2023 kl. 18:54</span> </span> <span class="minerva-icon minerva-icon-size-small minerva-icon--expand"></span> </div></a> <div class="post-content footer-content"> <div id="mw-data-after-content"> <div class="read-more-container"></div> </div> <div id="p-lang"> <h4>Språk</h4> <section> <ul id="p-variants" class="minerva-languages"></ul> <ul class="minerva-languages"> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://nn.wikipedia.org/wiki/Tregleiksmoment" title="Tregleiksmoment – norsk nynorsk" lang="nn" hreflang="nn" data-title="Tregleiksmoment" data-language-autonym="Norsk nynorsk" data-language-local-name="norsk nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li> <li class="interlanguage-link interwiki-da mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://da.wikipedia.org/wiki/Inertimoment" title="Inertimoment – dansk" lang="da" hreflang="da" data-title="Inertimoment" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li> <li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sv.wikipedia.org/wiki/Tr%25C3%25B6ghetsmoment" title="Tröghetsmoment – svensk" lang="sv" hreflang="sv" data-title="Tröghetsmoment" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li> <li class="interlanguage-link interwiki-is mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://is.wikipedia.org/wiki/Hverfitreg%25C3%25B0a" title="Hverfitregða – islandsk" lang="is" hreflang="is" data-title="Hverfitregða" data-language-autonym="Íslenska" data-language-local-name="islandsk" class="interlanguage-link-target"><span>Íslenska</span></a></li> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://af.wikipedia.org/wiki/Traagheidsmoment" title="Traagheidsmoment – afrikaans" lang="af" hreflang="af" data-title="Traagheidsmoment" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ar.wikipedia.org/wiki/%25D8%25B9%25D8%25B2%25D9%2585_%25D8%25A7%25D9%2584%25D9%2582%25D8%25B5%25D9%2588%25D8%25B1_%25D8%25A7%25D9%2584%25D8%25B0%25D8%25A7%25D8%25AA%25D9%258A" title="عزم القصور الذاتي – arabisk" lang="ar" hreflang="ar" data-title="عزم القصور الذاتي" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li> <li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ast.wikipedia.org/wiki/Momentu_d%2527inercia" title="Momentu d'inercia – asturisk" lang="ast" hreflang="ast" data-title="Momentu d'inercia" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li> <li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://bn.wikipedia.org/wiki/%25E0%25A6%259C%25E0%25A6%25A1%25E0%25A6%25BC%25E0%25A6%25A4%25E0%25A6%25BE%25E0%25A6%25B0_%25E0%25A6%25AD%25E0%25A7%258D%25E0%25A6%25B0%25E0%25A6%25BE%25E0%25A6%25AE%25E0%25A6%2595" title="জড়তার ভ্রামক – bengali" lang="bn" hreflang="bn" data-title="জড়তার ভ্রামক" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li> <li class="interlanguage-link interwiki-be mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://be.wikipedia.org/wiki/%25D0%259C%25D0%25BE%25D0%25BC%25D0%25B0%25D0%25BD%25D1%2582_%25D1%2596%25D0%25BD%25D0%25B5%25D1%2580%25D1%2586%25D1%258B%25D1%2596" title="Момант інерцыі – belarusisk" lang="be" hreflang="be" data-title="Момант інерцыі" data-language-autonym="Беларуская" data-language-local-name="belarusisk" class="interlanguage-link-target"><span>Беларуская</span></a></li> <li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://be-tarask.wikipedia.org/wiki/%25D0%259C%25D0%25BE%25D0%25BC%25D0%25B0%25D0%25BD%25D1%2582_%25D1%2596%25D0%25BD%25D1%258D%25D1%2580%25D1%2586%25D1%258B%25D1%2596" title="Момант інэрцыі – belarusisk (klassisk ortografi)" lang="be-tarask" hreflang="be-tarask" data-title="Момант інэрцыі" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusisk (klassisk ortografi)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li> <li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://bg.wikipedia.org/wiki/%25D0%259C%25D0%25B0%25D1%2581%25D0%25BE%25D0%25B2_%25D0%25B8%25D0%25BD%25D0%25B5%25D1%2580%25D1%2586%25D0%25B8%25D0%25BE%25D0%25BD%25D0%25B5%25D0%25BD_%25D0%25BC%25D0%25BE%25D0%25BC%25D0%25B5%25D0%25BD%25D1%2582" title="Масов инерционен момент – bulgarsk" lang="bg" hreflang="bg" data-title="Масов инерционен момент" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li> <li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://bs.wikipedia.org/wiki/Moment_inercije" title="Moment inercije – bosnisk" lang="bs" hreflang="bs" data-title="Moment inercije" data-language-autonym="Bosanski" data-language-local-name="bosnisk" class="interlanguage-link-target"><span>Bosanski</span></a></li> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ca.wikipedia.org/wiki/Moment_d%2527in%25C3%25A8rcia" title="Moment d'inèrcia – katalansk" lang="ca" hreflang="ca" data-title="Moment d'inèrcia" data-language-autonym="Català" data-language-local-name="katalansk" class="interlanguage-link-target"><span>Català</span></a></li> <li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://cv.wikipedia.org/wiki/%25D0%2598%25D0%25BD%25D0%25B5%25D1%2580%25D1%2586%25D0%25B8_%25D1%2581%25D0%25B0%25D0%25BC%25D0%25B0%25D0%25BD%25D1%2587%25C4%2595" title="Инерци саманчĕ – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Инерци саманчĕ" data-language-autonym="Чӑвашла" data-language-local-name="tsjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li> <li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://cs.wikipedia.org/wiki/Moment_setrva%25C4%258Dnosti" title="Moment setrvačnosti – tsjekkisk" lang="cs" hreflang="cs" data-title="Moment setrvačnosti" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li> <li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="anbefalt artikkel-merke"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://de.wikipedia.org/wiki/Tr%25C3%25A4gheitsmoment" title="Trägheitsmoment – tysk" lang="de" hreflang="de" data-title="Trägheitsmoment" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li> <li class="interlanguage-link interwiki-et mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://et.wikipedia.org/wiki/Inertsimoment" title="Inertsimoment – estisk" lang="et" hreflang="et" data-title="Inertsimoment" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li> <li class="interlanguage-link interwiki-el mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://el.wikipedia.org/wiki/%25CE%25A1%25CE%25BF%25CF%2580%25CE%25AE_%25CE%25B1%25CE%25B4%25CF%2581%25CE%25AC%25CE%25BD%25CE%25B5%25CE%25B9%25CE%25B1%25CF%2582" title="Ροπή αδράνειας – gresk" lang="el" hreflang="el" data-title="Ροπή αδράνειας" data-language-autonym="Ελληνικά" data-language-local-name="gresk" class="interlanguage-link-target"><span>Ελληνικά</span></a></li> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://en.wikipedia.org/wiki/Moment_of_inertia" title="Moment of inertia – engelsk" lang="en" hreflang="en" data-title="Moment of inertia" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li> <li class="interlanguage-link interwiki-es mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://es.wikipedia.org/wiki/Momento_de_inercia" title="Momento de inercia – spansk" lang="es" hreflang="es" data-title="Momento de inercia" data-language-autonym="Español" data-language-local-name="spansk" class="interlanguage-link-target"><span>Español</span></a></li> <li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://eo.wikipedia.org/wiki/Inercimomanto" title="Inercimomanto – esperanto" lang="eo" hreflang="eo" data-title="Inercimomanto" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li> <li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://eu.wikipedia.org/wiki/Inertzia-momentu" title="Inertzia-momentu – baskisk" lang="eu" hreflang="eu" data-title="Inertzia-momentu" data-language-autonym="Euskara" data-language-local-name="baskisk" class="interlanguage-link-target"><span>Euskara</span></a></li> <li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fa.wikipedia.org/wiki/%25DA%25AF%25D8%25B4%25D8%25AA%25D8%25A7%25D9%2588%25D8%25B1_%25D9%2584%25D8%25AE%25D8%25AA%25DB%258C" title="گشتاور لختی – persisk" lang="fa" hreflang="fa" data-title="گشتاور لختی" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li> <li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fr.wikipedia.org/wiki/Moment_d%2527inertie" title="Moment d'inertie – fransk" lang="fr" hreflang="fr" data-title="Moment d'inertie" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li> <li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ga.wikipedia.org/wiki/M%25C3%25B3imint_na_t%25C3%25A1imhe" title="Móimint na táimhe – irsk" lang="ga" hreflang="ga" data-title="Móimint na táimhe" data-language-autonym="Gaeilge" data-language-local-name="irsk" class="interlanguage-link-target"><span>Gaeilge</span></a></li> <li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://gl.wikipedia.org/wiki/Momento_de_inercia" title="Momento de inercia – galisisk" lang="gl" hreflang="gl" data-title="Momento de inercia" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li> <li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ko.wikipedia.org/wiki/%25EA%25B4%2580%25EC%2584%25B1_%25EB%25AA%25A8%25EB%25A9%2598%25ED%258A%25B8" title="관성 모멘트 – koreansk" lang="ko" hreflang="ko" data-title="관성 모멘트" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li> <li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://hy.wikipedia.org/wiki/%25D4%25BB%25D5%25B6%25D5%25A5%25D6%2580%25D6%2581%25D5%25AB%25D5%25A1%25D5%25B5%25D5%25AB_%25D5%25B4%25D5%25B8%25D5%25B4%25D5%25A5%25D5%25B6%25D5%25BF" title="Իներցիայի մոմենտ – armensk" lang="hy" hreflang="hy" data-title="Իներցիայի մոմենտ" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li> <li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://hi.wikipedia.org/wiki/%25E0%25A4%259C%25E0%25A4%25A1%25E0%25A4%25BC%25E0%25A4%25A4%25E0%25A5%258D%25E0%25A4%25B5%25E0%25A4%25BE%25E0%25A4%2598%25E0%25A5%2582%25E0%25A4%25B0%25E0%25A5%258D%25E0%25A4%25A3" title="जड़त्वाघूर्ण – hindi" lang="hi" hreflang="hi" data-title="जड़त्वाघूर्ण" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li> <li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://hr.wikipedia.org/wiki/Moment_inercije" title="Moment inercije – kroatisk" lang="hr" hreflang="hr" data-title="Moment inercije" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li> <li class="interlanguage-link interwiki-id mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://id.wikipedia.org/wiki/Momen_inersia" title="Momen inersia – indonesisk" lang="id" hreflang="id" data-title="Momen inersia" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li> <li class="interlanguage-link interwiki-it mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://it.wikipedia.org/wiki/Momento_di_inerzia" title="Momento di inerzia – italiensk" lang="it" hreflang="it" data-title="Momento di inerzia" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</span></a></li> <li class="interlanguage-link interwiki-he mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://he.wikipedia.org/wiki/%25D7%259E%25D7%2595%25D7%259E%25D7%25A0%25D7%2598_%25D7%2594%25D7%25AA%25D7%259E%25D7%2593" title="מומנט התמד – hebraisk" lang="he" hreflang="he" data-title="מומנט התמד" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li> <li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ka.wikipedia.org/wiki/%25E1%2583%2598%25E1%2583%259C%25E1%2583%2594%25E1%2583%25A0%25E1%2583%25AA%25E1%2583%2598%25E1%2583%2598%25E1%2583%25A1_%25E1%2583%259B%25E1%2583%259D%25E1%2583%259B%25E1%2583%2594%25E1%2583%259C%25E1%2583%25A2%25E1%2583%2598" title="ინერციის მომენტი – georgisk" lang="ka" hreflang="ka" data-title="ინერციის მომენტი" data-language-autonym="ქართული" data-language-local-name="georgisk" class="interlanguage-link-target"><span>ქართული</span></a></li> <li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://kk.wikipedia.org/wiki/%25D0%2598%25D0%25BD%25D0%25B5%25D1%2580%25D1%2586%25D0%25B8%25D1%258F_%25D0%25BC%25D0%25BE%25D0%25BC%25D0%25B5%25D0%25BD%25D1%2582%25D1%2596" title="Инерция моменті – kasakhisk" lang="kk" hreflang="kk" data-title="Инерция моменті" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li> <li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ht.wikipedia.org/wiki/Moman_in%25C3%25A8si" title="Moman inèsi – haitisk" lang="ht" hreflang="ht" data-title="Moman inèsi" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitisk" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li> <li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://lv.wikipedia.org/wiki/Inerces_moments" title="Inerces moments – latvisk" lang="lv" hreflang="lv" data-title="Inerces moments" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li> <li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://lt.wikipedia.org/wiki/Inercijos_momentas" title="Inercijos momentas – litauisk" lang="lt" hreflang="lt" data-title="Inercijos momentas" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li> <li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://hu.wikipedia.org/wiki/Tehetetlens%25C3%25A9gi_nyomat%25C3%25A9k" title="Tehetetlenségi nyomaték – ungarsk" lang="hu" hreflang="hu" data-title="Tehetetlenségi nyomaték" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li> <li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://mk.wikipedia.org/wiki/%25D0%259C%25D0%25BE%25D0%25BC%25D0%25B5%25D0%25BD%25D1%2582_%25D0%25BD%25D0%25B0_%25D0%25B8%25D0%25BD%25D0%25B5%25D1%2580%25D1%2586%25D0%25B8%25D1%2598%25D0%25B0" title="Момент на инерција – makedonsk" lang="mk" hreflang="mk" data-title="Момент на инерција" data-language-autonym="Македонски" data-language-local-name="makedonsk" class="interlanguage-link-target"><span>Македонски</span></a></li> <li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ml.wikipedia.org/wiki/%25E0%25B4%259C%25E0%25B4%25A2%25E0%25B4%25A4%25E0%25B5%258D%25E0%25B4%25B5%25E0%25B4%25BE%25E0%25B4%2598%25E0%25B5%2582%25E0%25B5%25BC%25E0%25B4%25A3%25E0%25B4%2582" title="ജഢത്വാഘൂർണം – malayalam" lang="ml" hreflang="ml" data-title="ജഢത്വാഘൂർണം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li> <li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ms.wikipedia.org/wiki/Momen_inersia" title="Momen inersia – malayisk" lang="ms" hreflang="ms" data-title="Momen inersia" data-language-autonym="Bahasa Melayu" data-language-local-name="malayisk" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li> <li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://nl.wikipedia.org/wiki/Traagheidsmoment" title="Traagheidsmoment – nederlandsk" lang="nl" hreflang="nl" data-title="Traagheidsmoment" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li> <li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ja.wikipedia.org/wiki/%25E6%2585%25A3%25E6%2580%25A7%25E3%2583%25A2%25E3%2583%25BC%25E3%2583%25A1%25E3%2583%25B3%25E3%2583%2588" title="慣性モーメント – japansk" lang="ja" hreflang="ja" data-title="慣性モーメント" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li> <li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://uz.wikipedia.org/wiki/Inersiya_momenti" title="Inersiya momenti – usbekisk" lang="uz" hreflang="uz" data-title="Inersiya momenti" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li> <li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://pl.wikipedia.org/wiki/Moment_bezw%25C5%2582adno%25C5%259Bci" title="Moment bezwładności – polsk" lang="pl" hreflang="pl" data-title="Moment bezwładności" data-language-autonym="Polski" data-language-local-name="polsk" class="interlanguage-link-target"><span>Polski</span></a></li> <li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://pt.wikipedia.org/wiki/Momento_de_in%25C3%25A9rcia" title="Momento de inércia – portugisisk" lang="pt" hreflang="pt" data-title="Momento de inércia" data-language-autonym="Português" data-language-local-name="portugisisk" class="interlanguage-link-target"><span>Português</span></a></li> <li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ro.wikipedia.org/wiki/Moment_de_iner%25C8%259Bie" title="Moment de inerție – rumensk" lang="ro" hreflang="ro" data-title="Moment de inerție" data-language-autonym="Română" data-language-local-name="rumensk" class="interlanguage-link-target"><span>Română</span></a></li> <li class="interlanguage-link interwiki-ru badge-Q17559452 badge-recommendedarticle mw-list-item" title="lovende artikkel"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ru.wikipedia.org/wiki/%25D0%259C%25D0%25BE%25D0%25BC%25D0%25B5%25D0%25BD%25D1%2582_%25D0%25B8%25D0%25BD%25D0%25B5%25D1%2580%25D1%2586%25D0%25B8%25D0%25B8" title="Момент инерции – russisk" lang="ru" hreflang="ru" data-title="Момент инерции" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li> <li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sq.wikipedia.org/wiki/Momenti_i_Inercis%25C3%25AB" title="Momenti i Inercisë – albansk" lang="sq" hreflang="sq" data-title="Momenti i Inercisë" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li> <li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://simple.wikipedia.org/wiki/Moment_of_inertia" title="Moment of inertia – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Moment of inertia" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" class="interlanguage-link-target"><span>Simple English</span></a></li> <li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sk.wikipedia.org/wiki/Moment_zotrva%25C4%258Dnosti" title="Moment zotrvačnosti – slovakisk" lang="sk" hreflang="sk" data-title="Moment zotrvačnosti" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" class="interlanguage-link-target"><span>Slovenčina</span></a></li> <li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sl.wikipedia.org/wiki/Vztrajnostni_moment" title="Vztrajnostni moment – slovensk" lang="sl" hreflang="sl" data-title="Vztrajnostni moment" data-language-autonym="Slovenščina" data-language-local-name="slovensk" class="interlanguage-link-target"><span>Slovenščina</span></a></li> <li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sr.wikipedia.org/wiki/%25D0%259C%25D0%25BE%25D0%25BC%25D0%25B5%25D0%25BD%25D1%2582_%25D0%25B8%25D0%25BD%25D0%25B5%25D1%2580%25D1%2586%25D0%25B8%25D1%2598%25D0%25B5" title="Момент инерције – serbisk" lang="sr" hreflang="sr" data-title="Момент инерције" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li> <li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://sh.wikipedia.org/wiki/Moment_inercije" title="Moment inercije – serbokroatisk" lang="sh" hreflang="sh" data-title="Moment inercije" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li> <li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://fi.wikipedia.org/wiki/Hitausmomentti" title="Hitausmomentti – finsk" lang="fi" hreflang="fi" data-title="Hitausmomentti" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li> <li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ta.wikipedia.org/wiki/%25E0%25AE%25A8%25E0%25AE%25BF%25E0%25AE%25B2%25E0%25AF%2588%25E0%25AE%25AE%25E0%25AE%25A4%25E0%25AF%258D_%25E0%25AE%25A4%25E0%25AE%25BF%25E0%25AE%25B0%25E0%25AF%2581%25E0%25AE%25AA%25E0%25AF%258D%25E0%25AE%25AA%25E0%25AF%2581%25E0%25AE%25A4%25E0%25AF%258D%25E0%25AE%25A4%25E0%25AE%25BF%25E0%25AE%25B1%25E0%25AE%25A9%25E0%25AF%258D" title="நிலைமத் திருப்புத்திறன் – tamil" lang="ta" hreflang="ta" data-title="நிலைமத் திருப்புத்திறன்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li> <li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://tt.wikipedia.org/wiki/%25C4%25B0nertsi%25C3%25A4_moment%25C4%25B1" title="İnertsiä momentı – tatarisk" lang="tt" hreflang="tt" data-title="İnertsiä momentı" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarisk" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li> <li class="interlanguage-link interwiki-th mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://th.wikipedia.org/wiki/%25E0%25B9%2582%25E0%25B8%25A1%25E0%25B9%2580%25E0%25B8%25A1%25E0%25B8%2599%25E0%25B8%2595%25E0%25B9%258C%25E0%25B8%2584%25E0%25B8%25A7%25E0%25B8%25B2%25E0%25B8%25A1%25E0%25B9%2580%25E0%25B8%2589%25E0%25B8%25B7%25E0%25B9%2588%25E0%25B8%25AD%25E0%25B8%25A2" title="โมเมนต์ความเฉื่อย – thai" lang="th" hreflang="th" data-title="โมเมนต์ความเฉื่อย" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li> <li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://tg.wikipedia.org/wiki/%25D0%259C%25D0%25BE%25D0%25BC%25D0%25B5%25D0%25BD%25D1%2582%25D0%25B8_%25D0%25B8%25D0%25BD%25D0%25B5%25D1%2580%25D1%2581%25D0%25B8%25D1%258F" title="Моменти инерсия – tadsjikisk" lang="tg" hreflang="tg" data-title="Моменти инерсия" data-language-autonym="Тоҷикӣ" data-language-local-name="tadsjikisk" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li> <li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://tr.wikipedia.org/wiki/Eylemsizlik_momenti" title="Eylemsizlik momenti – tyrkisk" lang="tr" hreflang="tr" data-title="Eylemsizlik momenti" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" class="interlanguage-link-target"><span>Türkçe</span></a></li> <li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://uk.wikipedia.org/wiki/%25D0%259C%25D0%25BE%25D0%25BC%25D0%25B5%25D0%25BD%25D1%2582_%25D1%2596%25D0%25BD%25D0%25B5%25D1%2580%25D1%2586%25D1%2596%25D1%2597" title="Момент інерції – ukrainsk" lang="uk" hreflang="uk" data-title="Момент інерції" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li> <li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://ur.wikipedia.org/wiki/%25D8%25AC%25D9%2585%25D9%2588%25D8%25AF_%25DA%25A9%25D8%25A7_%25D9%2585%25D8%25B9%25DB%258C%25D8%25A7%25D8%25B1_%25D8%25A7%25D8%25AB%25D8%25B1" title="جمود کا معیار اثر – urdu" lang="ur" hreflang="ur" data-title="جمود کا معیار اثر" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li> <li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://vi.wikipedia.org/wiki/M%25C3%25B4_men_qu%25C3%25A1n_t%25C3%25ADnh" title="Mô men quán tính – vietnamesisk" lang="vi" hreflang="vi" data-title="Mô men quán tính" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li> <li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://wuu.wikipedia.org/wiki/%25E8%25BD%25AC%25E5%258A%25A8%25E6%2583%25AF%25E9%2587%258F" title="转动惯量 – wu" lang="wuu" hreflang="wuu" data-title="转动惯量" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li> <li class="interlanguage-link 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