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Traagheidsmoment - Wikipedia
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<section class="mf-section-0" id="mf-section-0"> <p><b>Traagheidsmoment</b> is die mate waartoe 'n voorwerp traag is om rondom 'n as te versnel, en word dikwels voorgestel deur die letter <i>I</i>.</p> <figure typeof="mw:File/Thumb"> <a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Nik_Wallenda_Niagara_Falls_2012.jpg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Nik_Wallenda_Niagara_Falls_2012.jpg/250px-Nik_Wallenda_Niagara_Falls_2012.jpg" decoding="async" width="250" height="167" class="mw-file-element" srcset="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Nik_Wallenda_Niagara_Falls_2012.jpg/375px-Nik_Wallenda_Niagara_Falls_2012.jpg 1.5x,https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Nik_Wallenda_Niagara_Falls_2012.jpg/500px-Nik_Wallenda_Niagara_Falls_2012.jpg 2x" data-file-width="5184" data-file-height="3456"></a> <figcaption> 'n Persoon gebruik die groot traagheidsmoment van die staaf in sy hande om op 'n tou oor die Niagara-watervalle te loop. </figcaption> </figure> <figure typeof="mw:File/Thumb"> <a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Cup_of_Russia_2010_-_Yuko_Kawaguti_(2).jpg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/Cup_of_Russia_2010_-_Yuko_Kawaguti_%282%29.jpg/250px-Cup_of_Russia_2010_-_Yuko_Kawaguti_%282%29.jpg" decoding="async" width="250" height="407" class="mw-file-element" srcset="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/6/68/Cup_of_Russia_2010_-_Yuko_Kawaguti_%25282%2529.jpg 1.5x" data-file-width="307" data-file-height="500"></a> <figcaption> 'n Skaatser kan haar traagheidsmoment aanpas om vinniger of stadiger te spin deur haar arms in te trek of uit te strek. </figcaption> </figure> <p>Volgens <a href="https://af-m-wikipedia-org.translate.goog/wiki/Isaac_Newton?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Isaac Newton">Newton</a> se eerste bewegingswet, sal 'n voorwerp in rus bly of teen dieselfde lineêre snelheid beweeg tensy 'n eksterne netto krag daarop uitgeoefen word – die voorwerp se massa bied dus 'n traagheid om te versnel in 'n lineêre rigting. Traagheidsmoment kan gesien word as 'n analoog van hierdie traagheid van massa, maar wel op 'n voorwerp wat roteer. Dus sal 'n voorwerp wat rondom 'n as roteer in rus bly of teen dieselfde hoeksnelheid beweeg tensy 'n eksterne moment (of aksie wat rotasie veroorsaak) daarop inwerk.</p> <p>In algemene fisika is die definisie van 'n moment 'krag maal afstand',<sup id="cite_ref-1" class="reference"><a href="https://af-m-wikipedia-org.translate.goog/wiki/Traagheidsmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> en kan gesien word as enige aksie wat sal veroorsaak dat 'n voorwerp (of deeltjie binne in 'n voorwerp) rondom 'n as wil roteer. Die traagheidsmoment op enige deeltjie van 'n voorwerp is weer die massa van die deeltjie maal met die kwadraat van afstand van die as (of sentroïede) af. Die som van al die deeltjies se traagheidsmomente tel bymekaar om die traagheidsmoment van die totale voorwerp rondom die as te bepaal. Dus:</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=\sum _{i}m_{i}r_{i}^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <munder> <mo> ∑<!-- ∑ --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mi> i </mi> </mrow> </munder> <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> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I=\sum _{i}m_{i}r_{i}^{2}} </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62ebff911506a36540677baab2a84e659ebba1fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:12.955ex; height:5.509ex;" alt="{\displaystyle I=\sum _{i}m_{i}r_{i}^{2}}"></span>. </dd> </dl> <p>waarin</p> <ul> <li><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> <mspace width="thinmathspace"></mspace> </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/988f6ada07675268dc7164f44f469dbec6e00b8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.559ex; height:2.176ex;" alt="{\displaystyle I\,}"></span>: traagheidsmoment [eenheid kg.m²]</li> <li><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> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle m_{i}\,} </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb52186d95d67d5b73c19f41d63dadfa60b78ac0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.227ex; height:2.009ex;" alt="{\displaystyle m_{i}\,}"></span>: massa van deeltjie i [eenheid kg]</li> <li><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> <mspace width="thinmathspace"></mspace> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r_{i}\,} </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e25b2013fff765b56330cfd71d9acd2342d4ce5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.235ex; height:2.009ex;" alt="{\displaystyle r_{i}\,}"></span>: afstand van deeltjie i vanaf die as [eenheid m]</li> </ul> <p>Hoe verder 'n deeltjie dus van die as van die voorwerp af geleë is, hoe groter sal die bydrae tot die traagheidsmoment wees.</p> <p>Molekules in die gasfase kan vrylik roteer en hierdie rotasies is gekwantiseer. Oorgange tussen die verskillende rotasietoestande kan deur absorpsie van <a href="https://af-m-wikipedia-org.translate.goog/wiki/Mikrogolf?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Mikrogolf">mikrogolwe</a> waargeneem word en daardeur kan die molekule se traagheidsmomente bepaal word. (Daar is soms meer as een, as die deeltjie 'n vorm met lae simmetrie besit.)</p> </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="Traagheidsmomente_van_verskeie_liggame">Traagheidsmomente van verskeie liggame</h2><span class="mw-editsection"> <a role="button" href="https://af-m-wikipedia-org.translate.goog/w/index.php?title=Traagheidsmoment&action=edit&section=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wysig afdeling: Traagheidsmomente van verskeie liggame" 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>wysig</span> </a> </span> </div> <section class="mf-section-1 collapsible-block" id="mf-section-1"> <table class="wikitable"> <tbody> <tr> <th>Sketsvoorstelling</th> <th>Beskrywing</th> <th>Traagheidsmoment</th> </tr> <tr> <td><span class="mw-default-size" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_a_punktmasse.png?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit a punktmasse"> <noscript> <img alt="Traegheit a punktmasse" src="//upload.wikimedia.org/wikipedia/commons/b/b3/Traegheit_a_punktmasse.png" decoding="async" width="148" height="69" class="mw-file-element" data-file-width="148" data-file-height="69"> </noscript><span class="lazy-image-placeholder" style="width: 148px;height: 69px;" data-src="//upload.wikimedia.org/wikipedia/commons/b/b3/Traegheit_a_punktmasse.png" data-alt="Traegheit a punktmasse" data-width="148" data-height="69" data-class="mw-file-element"> </span></a></span></td> <td>'n massapunt op 'n afstand <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/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"> </noscript><span class="lazy-image-placeholder" style="width: 1.049ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" data-alt="{\displaystyle r}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> vanaf die draaias.</td> <td><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=m\cdot r^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I=m\cdot r^{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eec2a8c1ffe8ec639559ba3abb685488e282dabb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.093ex; height:2.676ex;" alt="{\displaystyle I=m\cdot r^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 10.093ex;height: 2.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eec2a8c1ffe8ec639559ba3abb685488e282dabb" data-alt="{\displaystyle I=m\cdot r^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td><span style="display:inline-block;width:0;">b)</span><span class="mw-valign-top" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_b_zylindermantel.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit b zylindermantel"> <noscript> <img alt="Traegheit b zylindermantel" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Traegheit_b_zylindermantel.svg/166px-Traegheit_b_zylindermantel.svg.png" decoding="async" width="166" height="103" class="mw-file-element" data-file-width="512" data-file-height="318"> </noscript><span class="lazy-image-placeholder" style="width: 166px;height: 103px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Traegheit_b_zylindermantel.svg/166px-Traegheit_b_zylindermantel.svg.png" data-alt="Traegheit b zylindermantel" data-width="166" data-height="103" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Traegheit_b_zylindermantel.svg/249px-Traegheit_b_zylindermantel.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Traegheit_b_zylindermantel.svg/332px-Traegheit_b_zylindermantel.svg.png 2x" data-class="mw-file-element"> </span></a></span></td> <td>'n silinder skil wat om sy silinderas draai.</td> <td><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=m\cdot r^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I=m\cdot r^{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eec2a8c1ffe8ec639559ba3abb685488e282dabb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.093ex; height:2.676ex;" alt="{\displaystyle I=m\cdot r^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 10.093ex;height: 2.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eec2a8c1ffe8ec639559ba3abb685488e282dabb" data-alt="{\displaystyle I=m\cdot r^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td><span style="display:inline-block;width:0;">c)</span><span class="mw-valign-top" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_c_vollzylinder.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit c vollzylinder"> <noscript> <img alt="Traegheit c vollzylinder" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Traegheit_c_vollzylinder.svg/166px-Traegheit_c_vollzylinder.svg.png" decoding="async" width="166" height="103" class="mw-file-element" data-file-width="512" data-file-height="318"> </noscript><span class="lazy-image-placeholder" style="width: 166px;height: 103px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Traegheit_c_vollzylinder.svg/166px-Traegheit_c_vollzylinder.svg.png" data-alt="Traegheit c vollzylinder" data-width="166" data-height="103" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Traegheit_c_vollzylinder.svg/249px-Traegheit_c_vollzylinder.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Traegheit_c_vollzylinder.svg/332px-Traegheit_c_vollzylinder.svg.png 2x" data-class="mw-file-element"> </span></a></span></td> <td>'n Soliede silinder wat om sy silinderas draai.</td> <td><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={\tfrac {1}{2}}m\cdot r^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I={\tfrac {1}{2}}m\cdot r^{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d96429a262cbaf3c537bb4080ffa1b18dc434308" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:11.751ex; height:3.509ex;" alt="{\displaystyle I={\tfrac {1}{2}}m\cdot r^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 11.751ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d96429a262cbaf3c537bb4080ffa1b18dc434308" data-alt="{\displaystyle I={\tfrac {1}{2}}m\cdot r^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td><span style="display:inline-block;width:0;">d)</span><span class="mw-valign-top" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_d_hohlzylinder2.svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit d hohlzylinder2"> <noscript> <img alt="Traegheit d hohlzylinder2" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Traegheit_d_hohlzylinder2.svg/166px-Traegheit_d_hohlzylinder2.svg.png" decoding="async" width="166" height="103" class="mw-file-element" data-file-width="512" data-file-height="318"> </noscript><span class="lazy-image-placeholder" style="width: 166px;height: 103px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Traegheit_d_hohlzylinder2.svg/166px-Traegheit_d_hohlzylinder2.svg.png" data-alt="Traegheit d hohlzylinder2" data-width="166" data-height="103" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Traegheit_d_hohlzylinder2.svg/249px-Traegheit_d_hohlzylinder2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Traegheit_d_hohlzylinder2.svg/332px-Traegheit_d_hohlzylinder2.svg.png 2x" data-class="mw-file-element"> </span></a></span></td> <td>'n hol silinder wat om sy as draai.</td> <td><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={\tfrac {1}{2}}m\cdot (r_{2}^{2}+r_{1}^{2})}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <mo stretchy="false"> ( </mo> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I={\tfrac {1}{2}}m\cdot (r_{2}^{2}+r_{1}^{2})} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a6b85fcb13c64b6ab8781567d69f4641fe12e93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.503ex; height:3.509ex;" alt="{\displaystyle I={\tfrac {1}{2}}m\cdot (r_{2}^{2}+r_{1}^{2})}"> </noscript><span class="lazy-image-placeholder" style="width: 18.503ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a6b85fcb13c64b6ab8781567d69f4641fe12e93" data-alt="{\displaystyle I={\tfrac {1}{2}}m\cdot (r_{2}^{2}+r_{1}^{2})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span><sup id="cite_ref-2" class="reference"><a href="https://af-m-wikipedia-org.translate.goog/wiki/Traagheidsmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><br> (m: massa van die hol silinder)</td> </tr> <tr> <td><span class="mw-default-size" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_e_vollzylinder_2.png?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit e vollzylinder 2"> <noscript> <img alt="Traegheit e vollzylinder 2" src="//upload.wikimedia.org/wikipedia/commons/2/29/Traegheit_e_vollzylinder_2.png" decoding="async" width="154" height="141" class="mw-file-element" data-file-width="154" data-file-height="141"> </noscript><span class="lazy-image-placeholder" style="width: 154px;height: 141px;" data-src="//upload.wikimedia.org/wikipedia/commons/2/29/Traegheit_e_vollzylinder_2.png" data-alt="Traegheit e vollzylinder 2" data-width="154" data-height="141" data-class="mw-file-element"> </span></a></span></td> <td>'n Vol silinder wat roteer rondom 'n simmetriese as in die middel van sy lengte.</td> <td><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={\tfrac {1}{4}}m\cdot r^{2}+{\tfrac {1}{12}}m\cdot l^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> l </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I={\tfrac {1}{4}}m\cdot r^{2}+{\tfrac {1}{12}}m\cdot l^{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5c6ba12721bdf37ebffba408ba10d2ef84b846f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:22.538ex; height:3.509ex;" alt="{\displaystyle I={\tfrac {1}{4}}m\cdot r^{2}+{\tfrac {1}{12}}m\cdot l^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 22.538ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5c6ba12721bdf37ebffba408ba10d2ef84b846f" data-alt="{\displaystyle I={\tfrac {1}{4}}m\cdot r^{2}+{\tfrac {1}{12}}m\cdot l^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td><span class="mw-default-size" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_f_zylindermantel_2.png?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit f zylindermantel 2"> <noscript> <img alt="Traegheit f zylindermantel 2" src="//upload.wikimedia.org/wikipedia/commons/c/ca/Traegheit_f_zylindermantel_2.png" decoding="async" width="154" height="141" class="mw-file-element" data-file-width="154" data-file-height="141"> </noscript><span class="lazy-image-placeholder" style="width: 154px;height: 141px;" data-src="//upload.wikimedia.org/wikipedia/commons/c/ca/Traegheit_f_zylindermantel_2.png" data-alt="Traegheit f zylindermantel 2" data-width="154" data-height="141" data-class="mw-file-element"> </span></a></span></td> <td>'n silinder skil wat roteer rondom 'n simmetriese as in die middel van sy lengte.</td> <td><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={\tfrac {1}{2}}m\cdot r^{2}+{\tfrac {1}{12}}m\cdot l^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> l </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I={\tfrac {1}{2}}m\cdot r^{2}+{\tfrac {1}{12}}m\cdot l^{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/671e54da80aa44abc488a6c26e1a3a0f43dc8b27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:22.538ex; height:3.509ex;" alt="{\displaystyle I={\tfrac {1}{2}}m\cdot r^{2}+{\tfrac {1}{12}}m\cdot l^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 22.538ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/671e54da80aa44abc488a6c26e1a3a0f43dc8b27" data-alt="{\displaystyle I={\tfrac {1}{2}}m\cdot r^{2}+{\tfrac {1}{12}}m\cdot l^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td><span class="mw-default-size" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_g_stab1.png?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit g stab1"> <noscript> <img alt="Traegheit g stab1" src="//upload.wikimedia.org/wikipedia/commons/1/18/Traegheit_g_stab1.png" decoding="async" width="145" height="84" class="mw-file-element" data-file-width="145" data-file-height="84"> </noscript><span class="lazy-image-placeholder" style="width: 145px;height: 84px;" data-src="//upload.wikimedia.org/wikipedia/commons/1/18/Traegheit_g_stab1.png" data-alt="Traegheit g stab1" data-width="145" data-height="84" data-class="mw-file-element"> </span></a></span></td> <td>'n Dun staaf wat roteer rondom 'n simmetriese as in die middel van sy lengte. (Let op dat hierdie formule 'n benadering is van die silinder met de aanname dat <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\ll l}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> r </mi> <mo> ≪<!-- ≪ --> </mo> <mi> l </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle r\ll l} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49fd9e8d7c3e07b8cd684df5b6b0826c74b026d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.356ex; height:2.176ex;" alt="{\displaystyle r\ll l}"> </noscript><span class="lazy-image-placeholder" style="width: 5.356ex;height: 2.176ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49fd9e8d7c3e07b8cd684df5b6b0826c74b026d1" data-alt="{\displaystyle r\ll l}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>)</td> <td><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={\tfrac {1}{12}}m\cdot l^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> l </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I={\tfrac {1}{12}}m\cdot l^{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87b55ca95b4db804f9d7a044ef528eee41aa5b64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:12.217ex; height:3.509ex;" alt="{\displaystyle I={\tfrac {1}{12}}m\cdot l^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 12.217ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87b55ca95b4db804f9d7a044ef528eee41aa5b64" data-alt="{\displaystyle I={\tfrac {1}{12}}m\cdot l^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td><span class="mw-default-size" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_h_stab2.png?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit h stab2"> <noscript> <img alt="Traegheit h stab2" src="//upload.wikimedia.org/wikipedia/commons/7/7f/Traegheit_h_stab2.png" decoding="async" width="145" height="84" class="mw-file-element" data-file-width="145" data-file-height="84"> </noscript><span class="lazy-image-placeholder" style="width: 145px;height: 84px;" data-src="//upload.wikimedia.org/wikipedia/commons/7/7f/Traegheit_h_stab2.png" data-alt="Traegheit h stab2" data-width="145" data-height="84" data-class="mw-file-element"> </span></a></span></td> <td>'n Dun staaf wat draai rondom een van sy endpunte.</td> <td><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={\tfrac {1}{3}}m\cdot l^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> l </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I={\tfrac {1}{3}}m\cdot l^{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce90a4b9dbddc2b0a63534e47a31fecfdc2a0604" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:11.395ex; height:3.676ex;" alt="{\displaystyle I={\tfrac {1}{3}}m\cdot l^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 11.395ex;height: 3.676ex;vertical-align: -1.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce90a4b9dbddc2b0a63534e47a31fecfdc2a0604" data-alt="{\displaystyle I={\tfrac {1}{3}}m\cdot l^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td><span class="mw-default-size" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_i_kugel1.png?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit i kugel1"> <noscript> <img alt="Traegheit i kugel1" src="//upload.wikimedia.org/wikipedia/commons/c/c4/Traegheit_i_kugel1.png" decoding="async" width="154" height="141" class="mw-file-element" data-file-width="154" data-file-height="141"> </noscript><span class="lazy-image-placeholder" style="width: 154px;height: 141px;" data-src="//upload.wikimedia.org/wikipedia/commons/c/c4/Traegheit_i_kugel1.png" data-alt="Traegheit i kugel1" data-width="154" data-height="141" data-class="mw-file-element"> </span></a></span></td> <td>'n Hol sfeer, met 'n weglaatbare dikte en 'n willekeurige draaias deur die middelpunt.</td> <td><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={\tfrac {2}{3}}m\cdot r^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I={\tfrac {2}{3}}m\cdot r^{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a3acd317cf3f8a7e7f5183ed55934cc6f41f55f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:11.751ex; height:3.676ex;" alt="{\displaystyle I={\tfrac {2}{3}}m\cdot r^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 11.751ex;height: 3.676ex;vertical-align: -1.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a3acd317cf3f8a7e7f5183ed55934cc6f41f55f" data-alt="{\displaystyle I={\tfrac {2}{3}}m\cdot r^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td><span class="mw-default-size" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_j_kugel1.png?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit j kugel1"> <noscript> <img alt="Traegheit j kugel1" src="//upload.wikimedia.org/wikipedia/commons/f/f5/Traegheit_j_kugel1.png" decoding="async" width="154" height="141" class="mw-file-element" data-file-width="154" data-file-height="141"> </noscript><span class="lazy-image-placeholder" style="width: 154px;height: 141px;" data-src="//upload.wikimedia.org/wikipedia/commons/f/f5/Traegheit_j_kugel1.png" data-alt="Traegheit j kugel1" data-width="154" data-height="141" data-class="mw-file-element"> </span></a></span></td> <td>'n Soliede sfeer, met 'n willekeurige draaias deur die middelpunt.</td> <td><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={\tfrac {2}{5}}m\cdot r^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 2 </mn> <mn> 5 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I={\tfrac {2}{5}}m\cdot r^{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b1b020d5d627b464b3f5a32b20994db7e1ecc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:11.751ex; height:3.676ex;" alt="{\displaystyle I={\tfrac {2}{5}}m\cdot r^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 11.751ex;height: 3.676ex;vertical-align: -1.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b1b020d5d627b464b3f5a32b20994db7e1ecc0" data-alt="{\displaystyle I={\tfrac {2}{5}}m\cdot r^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td><span class="mw-default-size" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Traegheit_k_quader.png?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Traegheit k quader"> <noscript> <img alt="Traegheit k quader" src="//upload.wikimedia.org/wikipedia/commons/4/4e/Traegheit_k_quader.png" decoding="async" width="114" height="133" class="mw-file-element" data-file-width="114" data-file-height="133"> </noscript><span class="lazy-image-placeholder" style="width: 114px;height: 133px;" data-src="//upload.wikimedia.org/wikipedia/commons/4/4e/Traegheit_k_quader.png" data-alt="Traegheit k quader" data-width="114" data-height="133" data-class="mw-file-element"> </span></a></span></td> <td>'n Plaat met lengtes a en b, met die draaias loodreg op die plaat (vergelyk dun ronde staaf).</td> <td><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={\tfrac {1}{12}}m\cdot (a^{2}+b^{2})}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> I </mi> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo> ⋅<!-- ⋅ --> </mo> <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> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I={\tfrac {1}{12}}m\cdot (a^{2}+b^{2})} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6d4869600cd2d191fb0c99a52ab34c69d5b5993" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:19.455ex; height:3.509ex;" alt="{\displaystyle I={\tfrac {1}{12}}m\cdot (a^{2}+b^{2})}"> </noscript><span class="lazy-image-placeholder" style="width: 19.455ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6d4869600cd2d191fb0c99a52ab34c69d5b5993" data-alt="{\displaystyle I={\tfrac {1}{12}}m\cdot (a^{2}+b^{2})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td></td> <td>Dun skyf, straal <i>r</i> en massa <i>m</i> (gelyk aan soliede silinder).</td> <td><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_{z}={\tfrac {1}{2}}mr^{2}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> z </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{z}={\tfrac {1}{2}}mr^{2}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1230c3cec34073404cc6042f0cba82b0f8a2eb85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:10.925ex; height:3.509ex;" alt="{\displaystyle I_{z}={\tfrac {1}{2}}mr^{2}}"> </noscript><span class="lazy-image-placeholder" style="width: 10.925ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1230c3cec34073404cc6042f0cba82b0f8a2eb85" data-alt="{\displaystyle I_{z}={\tfrac {1}{2}}mr^{2}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span><br><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_{x}=I_{y}={\tfrac {1}{4}}m(r^{2})}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> = </mo> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo stretchy="false"> ( </mo> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{x}=I_{y}={\tfrac {1}{4}}m(r^{2})} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87640bb8f62fb748a3d99b0915d97c615270442" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.076ex; height:3.509ex;" alt="{\displaystyle I_{x}=I_{y}={\tfrac {1}{4}}m(r^{2})}"> </noscript><span class="lazy-image-placeholder" style="width: 18.076ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87640bb8f62fb748a3d99b0915d97c615270442" data-alt="{\displaystyle I_{x}=I_{y}={\tfrac {1}{4}}m(r^{2})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td><span class="mw-default-size" typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/L%C3%AAer:Cone_(geometry).svg?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-file-description" title="Cone (geometry)"> <noscript> <img alt="Cone (geometry)" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Cone_%28geometry%29.svg/201px-Cone_%28geometry%29.svg.png" decoding="async" width="201" height="360" class="mw-file-element" data-file-width="201" data-file-height="360"> </noscript><span class="lazy-image-placeholder" style="width: 201px;height: 360px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Cone_%28geometry%29.svg/201px-Cone_%28geometry%29.svg.png" data-alt="Cone (geometry)" data-width="201" data-height="360" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Cone_%28geometry%29.svg/302px-Cone_%28geometry%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Cone_%28geometry%29.svg/402px-Cone_%28geometry%29.svg.png 2x" data-class="mw-file-element"> </span></a></span></td> <td>'n Kegel, straal <i>r</i>, hoogte <i>h</i>, en massa <i>m</i>.</td> <td><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_{z}={\tfrac {3}{10}}mr^{2}\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> z </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 3 </mn> <mn> 10 </mn> </mfrac> </mstyle> </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_{z}={\tfrac {3}{10}}mr^{2}\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af2f3e7bc6c859acc44c958339a2784738148d6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; margin-right: -0.387ex; width:12.134ex; height:3.676ex;" alt="{\displaystyle I_{z}={\tfrac {3}{10}}mr^{2}\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 12.134ex;height: 3.676ex;vertical-align: -1.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af2f3e7bc6c859acc44c958339a2784738148d6d" data-alt="{\displaystyle I_{z}={\tfrac {3}{10}}mr^{2}\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span><br><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_{x}=I_{y}={\tfrac {3}{5}}m({\tfrac {1}{4}}r^{2}+h^{2})\,\!}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> x </mi> </mrow> </msub> <mo> = </mo> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> y </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 3 </mn> <mn> 5 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo stretchy="false"> ( </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mstyle> </mrow> <msup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <msup> <mi> h </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_{x}=I_{y}={\tfrac {3}{5}}m({\tfrac {1}{4}}r^{2}+h^{2})\,\!} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc9cb86ef3e259cd228703754b8d0c6617602d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; margin-right: -0.387ex; width:25.354ex; height:3.676ex;" alt="{\displaystyle I_{x}=I_{y}={\tfrac {3}{5}}m({\tfrac {1}{4}}r^{2}+h^{2})\,\!}"> </noscript><span class="lazy-image-placeholder" style="width: 25.354ex;height: 3.676ex;vertical-align: -1.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc9cb86ef3e259cd228703754b8d0c6617602d6" data-alt="{\displaystyle I_{x}=I_{y}={\tfrac {3}{5}}m({\tfrac {1}{4}}r^{2}+h^{2})\,\!}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> <tr> <td></td> <td>Soliede balk, hoogte <i>h</i>, breedte <i>b</i>, diepte <i>d</i> en massa <i>m</i> (vergelyk plaat).</td> <td><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_{h}={\tfrac {1}{12}}m(b^{2}+d^{2})}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> h </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo stretchy="false"> ( </mo> <msup> <mi> b </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <msup> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{h}={\tfrac {1}{12}}m(b^{2}+d^{2})} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/159658fc994af0dbda8ce34cabc9b89b5ac44a09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.795ex; height:3.509ex;" alt="{\displaystyle I_{h}={\tfrac {1}{12}}m(b^{2}+d^{2})}"> </noscript><span class="lazy-image-placeholder" style="width: 18.795ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/159658fc994af0dbda8ce34cabc9b89b5ac44a09" data-alt="{\displaystyle I_{h}={\tfrac {1}{12}}m(b^{2}+d^{2})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span><br><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_{b}={\tfrac {1}{12}}m(h^{2}+d^{2})}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> b </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo stretchy="false"> ( </mo> <msup> <mi> h </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo> + </mo> <msup> <mi> d </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msup> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{b}={\tfrac {1}{12}}m(h^{2}+d^{2})} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a56c174fc827efd6868704462fa9bc70d117276" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.895ex; height:3.509ex;" alt="{\displaystyle I_{b}={\tfrac {1}{12}}m(h^{2}+d^{2})}"> </noscript><span class="lazy-image-placeholder" style="width: 18.895ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a56c174fc827efd6868704462fa9bc70d117276" data-alt="{\displaystyle I_{b}={\tfrac {1}{12}}m(h^{2}+d^{2})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span><br><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_{d}={\tfrac {1}{12}}m(h^{2}+b^{2})}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> d </mi> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo stretchy="false"> ( </mo> <msup> <mi> h </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> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{d}={\tfrac {1}{12}}m(h^{2}+b^{2})} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a8ca6d1fb445a05c46727a272d9f2179945f568" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:18.829ex; height:3.509ex;" alt="{\displaystyle I_{d}={\tfrac {1}{12}}m(h^{2}+b^{2})}"> </noscript><span class="lazy-image-placeholder" style="width: 18.829ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a8ca6d1fb445a05c46727a272d9f2179945f568" data-alt="{\displaystyle I_{d}={\tfrac {1}{12}}m(h^{2}+b^{2})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></td> </tr> </tbody> </table> </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="Verwysings">Verwysings</h2><span class="mw-editsection"> <a role="button" href="https://af-m-wikipedia-org.translate.goog/w/index.php?title=Traagheidsmoment&action=edit&section=2&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wysig afdeling: Verwysings" 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>wysig</span> </a> </span> </div> <section class="mf-section-2 collapsible-block" id="mf-section-2"> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="https://af-m-wikipedia-org.translate.goog/wiki/Traagheidsmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-1">↑</a></span> <span class="reference-text">Allen, JH. 2010. Statics for dummies. John Wiley and Sons</span></li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="https://af-m-wikipedia-org.translate.goog/wiki/Traagheidsmoment?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-2">↑</a></span> <span class="reference-text">Die traagheidsmoment van 'n hol silinder kan ook as volg bepaal word: <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 {hol} }=I_{\mathrm {gr} }-I_{\mathrm {kl} }={\tfrac {1}{2}}\rho \pi hr_{2}^{4}-{\tfrac {1}{2}}\rho \pi hr_{1}^{4}={\tfrac {1}{2}}\rho \pi h(r_{2}^{2}-r_{1}^{2})(r_{2}^{2}+r_{1}^{2})={\tfrac {1}{2}}m(r_{2}^{2}+r_{1}^{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"> h </mi> <mi mathvariant="normal"> o </mi> <mi mathvariant="normal"> l </mi> </mrow> </mrow> </msub> <mo> = </mo> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> g </mi> <mi mathvariant="normal"> r </mi> </mrow> </mrow> </msub> <mo> −<!-- − --> </mo> <msub> <mi> I </mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> k </mi> <mi mathvariant="normal"> l </mi> </mrow> </mrow> </msub> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mstyle> </mrow> <mi> ρ<!-- ρ --> </mi> <mi> π<!-- π --> </mi> <mi> h </mi> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 4 </mn> </mrow> </msubsup> <mo> −<!-- − --> </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mstyle> </mrow> <mi> ρ<!-- ρ --> </mi> <mi> π<!-- π --> </mi> <mi> h </mi> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 4 </mn> </mrow> </msubsup> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mstyle> </mrow> <mi> ρ<!-- ρ --> </mi> <mi> π<!-- π --> </mi> <mi> h </mi> <mo stretchy="false"> ( </mo> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> −<!-- − --> </mo> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo stretchy="false"> ) </mo> <mo stretchy="false"> ( </mo> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo stretchy="false"> ) </mo> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mstyle> </mrow> <mi> m </mi> <mo stretchy="false"> ( </mo> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo> + </mo> <msubsup> <mi> r </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msubsup> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle I_{\mathrm {hol} }=I_{\mathrm {gr} }-I_{\mathrm {kl} }={\tfrac {1}{2}}\rho \pi hr_{2}^{4}-{\tfrac {1}{2}}\rho \pi hr_{1}^{4}={\tfrac {1}{2}}\rho \pi h(r_{2}^{2}-r_{1}^{2})(r_{2}^{2}+r_{1}^{2})={\tfrac {1}{2}}m(r_{2}^{2}+r_{1}^{2})} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81fcaec276d67de54827330afa1248c1f5f4af14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:77.89ex; height:3.509ex;" alt="{\displaystyle I_{\mathrm {hol} }=I_{\mathrm {gr} }-I_{\mathrm {kl} }={\tfrac {1}{2}}\rho \pi hr_{2}^{4}-{\tfrac {1}{2}}\rho \pi hr_{1}^{4}={\tfrac {1}{2}}\rho \pi h(r_{2}^{2}-r_{1}^{2})(r_{2}^{2}+r_{1}^{2})={\tfrac {1}{2}}m(r_{2}^{2}+r_{1}^{2})}"> </noscript><span class="lazy-image-placeholder" style="width: 77.89ex;height: 3.509ex;vertical-align: -1.171ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81fcaec276d67de54827330afa1248c1f5f4af14" data-alt="{\displaystyle I_{\mathrm {hol} }=I_{\mathrm {gr} }-I_{\mathrm {kl} }={\tfrac {1}{2}}\rho \pi hr_{2}^{4}-{\tfrac {1}{2}}\rho \pi hr_{1}^{4}={\tfrac {1}{2}}\rho \pi h(r_{2}^{2}-r_{1}^{2})(r_{2}^{2}+r_{1}^{2})={\tfrac {1}{2}}m(r_{2}^{2}+r_{1}^{2})}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></span></li> </ol> </div> <div class="notice metadata plainlinks" id="saadjie"> <span typeof="mw:File"><a href="https://af-m-wikipedia-org.translate.goog/wiki/Wikipedia:Saadjie?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wikipedia:Saadjie"> <noscript> <img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/45px-Wiki_letter_w.svg.png" decoding="async" width="45" height="45" class="mw-file-element" data-file-width="44" data-file-height="44"> </noscript><span class="lazy-image-placeholder" style="width: 45px;height: 45px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/45px-Wiki_letter_w.svg.png" data-width="45" data-height="45" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/68px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/90px-Wiki_letter_w.svg.png 2x" data-class="mw-file-element"> </span></a></span> <i>Hierdie artikel is ’n <a href="https://af-m-wikipedia-org.translate.goog/wiki/Wikipedia:Saadjie?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wikipedia:Saadjie">saadjie</a>. Voel vry om Wikipedia te help deur dit <a class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://af.wikipedia.org/w/index.php?title%3DTraagheidsmoment%26action%3Dedit">uit te brei</a>.</i> </div><!-- NewPP limit report Parsed by mw‐web.eqiad.main‐7c55db6c78‐lts6k Cached time: 20241027145720 Cache expiry: 2592000 Reduced expiry: false Complications: [] CPU time usage: 0.116 seconds Real time usage: 0.432 seconds Preprocessor visited node count: 261/1000000 Post‐expand include size: 4022/2097152 bytes Template argument size: 0/2097152 bytes Highest expansion depth: 5/100 Expensive parser function count: 4/500 Unstrip recursion depth: 1/20 Unstrip post‐expand size: 1654/5000000 bytes Lua time usage: 0.030/10.000 seconds Lua memory usage: 1132770/52428800 bytes Number of Wikibase entities loaded: 1/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 75.283 1 -total 91.94% 69.218 1 Sjabloon:Normdata 5.05% 3.800 1 Sjabloon:Verwysings 2.82% 2.122 1 Sjabloon:Saadjie --> <!-- Saved in parser cache with key afwiki:pcache:idhash:73458-0!canonical and timestamp 20241027145720 and revision id 2593581. 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data-title="Момант інерцыі" data-language-autonym="Беларуская" data-language-local-name="Belarussies" 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 – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Момант інэрцыі" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" 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 – Bulgaars" lang="bg" hreflang="bg" data-title="Масов инерционен момент" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</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 – Bengaals" lang="bn" hreflang="bn" data-title="জড়তার ভ্রামক" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</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 – Bosnies" lang="bs" hreflang="bs" data-title="Moment inercije" data-language-autonym="Bosanski" data-language-local-name="Bosnies" 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 – Katalaans" lang="ca" hreflang="ca" data-title="Moment d'inèrcia" data-language-autonym="Català" data-language-local-name="Katalaans" class="interlanguage-link-target"><span>Català</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 – Tsjeggies" lang="cs" hreflang="cs" data-title="Moment setrvačnosti" data-language-autonym="Čeština" data-language-local-name="Tsjeggies" class="interlanguage-link-target"><span>Čeština</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 – Chuvash" lang="cv" hreflang="cv" data-title="Инерци саманчĕ" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</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 – Deens" lang="da" hreflang="da" data-title="Inertimoment" data-language-autonym="Dansk" data-language-local-name="Deens" class="interlanguage-link-target"><span>Dansk</span></a></li> <li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><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 – Duits" lang="de" hreflang="de" data-title="Trägheitsmoment" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</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 – Grieks" lang="el" hreflang="el" data-title="Ροπή αδράνειας" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" 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 – Engels" lang="en" hreflang="en" data-title="Moment of inertia" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</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-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 – Spaans" lang="es" hreflang="es" data-title="Momento de inercia" data-language-autonym="Español" data-language-local-name="Spaans" class="interlanguage-link-target"><span>Español</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 – Estnies" lang="et" hreflang="et" data-title="Inertsimoment" data-language-autonym="Eesti" data-language-local-name="Estnies" class="interlanguage-link-target"><span>Eesti</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 – Baskies" lang="eu" hreflang="eu" data-title="Inertzia-momentu" data-language-autonym="Euskara" data-language-local-name="Baskies" 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 – Persies" lang="fa" hreflang="fa" data-title="گشتاور لختی" data-language-autonym="فارسی" data-language-local-name="Persies" class="interlanguage-link-target"><span>فارسی</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 – Fins" lang="fi" hreflang="fi" data-title="Hitausmomentti" data-language-autonym="Suomi" data-language-local-name="Fins" class="interlanguage-link-target"><span>Suomi</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 – Frans" lang="fr" hreflang="fr" data-title="Moment d'inertie" data-language-autonym="Français" data-language-local-name="Frans" 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 – Iers" lang="ga" hreflang="ga" data-title="Móimint na táimhe" data-language-autonym="Gaeilge" data-language-local-name="Iers" 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 – Galisies" lang="gl" hreflang="gl" data-title="Momento de inercia" data-language-autonym="Galego" data-language-local-name="Galisies" class="interlanguage-link-target"><span>Galego</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 – Hebreeus" lang="he" hreflang="he" data-title="מומנט התמד" data-language-autonym="עברית" data-language-local-name="Hebreeus" class="interlanguage-link-target"><span>עברית</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 – Kroaties" lang="hr" hreflang="hr" data-title="Moment inercije" data-language-autonym="Hrvatski" data-language-local-name="Kroaties" class="interlanguage-link-target"><span>Hrvatski</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 – Haïtiaans" lang="ht" hreflang="ht" data-title="Moman inèsi" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haïtiaans" class="interlanguage-link-target"><span>Kreyòl ayisyen</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 – Hongaars" lang="hu" hreflang="hu" data-title="Tehetetlenségi nyomaték" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</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 – Armeens" lang="hy" hreflang="hy" data-title="Իներցիայի մոմենտ" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</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 – Indonesies" lang="id" hreflang="id" data-title="Momen inersia" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesies" class="interlanguage-link-target"><span>Bahasa Indonesia</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 – Yslands" lang="is" hreflang="is" data-title="Hverfitregða" data-language-autonym="Íslenska" data-language-local-name="Yslands" class="interlanguage-link-target"><span>Íslenska</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 – Italiaans" lang="it" hreflang="it" data-title="Momento di inerzia" data-language-autonym="Italiano" data-language-local-name="Italiaans" class="interlanguage-link-target"><span>Italiano</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 – Japannees" lang="ja" hreflang="ja" data-title="慣性モーメント" data-language-autonym="日本語" data-language-local-name="Japannees" class="interlanguage-link-target"><span>日本語</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 – Georgies" lang="ka" hreflang="ka" data-title="ინერციის მომენტი" data-language-autonym="ქართული" data-language-local-name="Georgies" 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 – Kazaks" lang="kk" hreflang="kk" data-title="Инерция моменті" data-language-autonym="Қазақша" data-language-local-name="Kazaks" class="interlanguage-link-target"><span>Қазақша</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 – Koreaans" lang="ko" hreflang="ko" data-title="관성 모멘트" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</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 – Litaus" lang="lt" hreflang="lt" data-title="Inercijos momentas" data-language-autonym="Lietuvių" data-language-local-name="Litaus" class="interlanguage-link-target"><span>Lietuvių</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 – Letties" lang="lv" hreflang="lv" data-title="Inerces moments" data-language-autonym="Latviešu" data-language-local-name="Letties" class="interlanguage-link-target"><span>Latviešu</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 – Masedonies" lang="mk" hreflang="mk" data-title="Момент на инерција" data-language-autonym="Македонски" data-language-local-name="Masedonies" 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 – Malabaars" lang="ml" hreflang="ml" data-title="ജഢത്വാഘൂർണം" data-language-autonym="മലയാളം" data-language-local-name="Malabaars" 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 – Maleis" lang="ms" hreflang="ms" data-title="Momen inersia" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" 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 – Nederlands" lang="nl" hreflang="nl" data-title="Traagheidsmoment" data-language-autonym="Nederlands" data-language-local-name="Nederlands" class="interlanguage-link-target"><span>Nederlands</span></a></li> <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 – Nuwe Noors" lang="nn" hreflang="nn" data-title="Tregleiksmoment" data-language-autonym="Norsk nynorsk" data-language-local-name="Nuwe Noors" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li> <li class="interlanguage-link interwiki-no mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://no.wikipedia.org/wiki/Treghetsmoment" title="Treghetsmoment – Boeknoors" lang="nb" hreflang="nb" data-title="Treghetsmoment" data-language-autonym="Norsk bokmål" data-language-local-name="Boeknoors" class="interlanguage-link-target"><span>Norsk bokmål</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 – Pools" lang="pl" hreflang="pl" data-title="Moment bezwładności" data-language-autonym="Polski" data-language-local-name="Pools" 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 – Portugees" lang="pt" hreflang="pt" data-title="Momento de inércia" data-language-autonym="Português" data-language-local-name="Portugees" 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 – Roemeens" lang="ro" hreflang="ro" data-title="Moment de inerție" data-language-autonym="Română" data-language-local-name="Roemeens" class="interlanguage-link-target"><span>Română</span></a></li> <li class="interlanguage-link interwiki-ru badge-Q17559452 badge-recommendedarticle mw-list-item" title="recommended article"><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 – Russies" lang="ru" hreflang="ru" data-title="Момент инерции" data-language-autonym="Русский" data-language-local-name="Russies" class="interlanguage-link-target"><span>Русский</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 – Serwo-Kroaties" lang="sh" hreflang="sh" data-title="Moment inercije" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serwo-Kroaties" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</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 – Simple English" lang="en-simple" hreflang="en-simple" data-title="Moment of inertia" data-language-autonym="Simple English" data-language-local-name="Simple English" 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 – Slowaaks" lang="sk" hreflang="sk" data-title="Moment zotrvačnosti" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" 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 – Sloweens" lang="sl" hreflang="sl" data-title="Vztrajnostni moment" data-language-autonym="Slovenščina" data-language-local-name="Sloweens" class="interlanguage-link-target"><span>Slovenščina</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 – Albanees" lang="sq" hreflang="sq" data-title="Momenti i Inercisë" data-language-autonym="Shqip" data-language-local-name="Albanees" class="interlanguage-link-target"><span>Shqip</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 – Serwies" lang="sr" hreflang="sr" data-title="Момент инерције" data-language-autonym="Српски / srpski" data-language-local-name="Serwies" class="interlanguage-link-target"><span>Српски / srpski</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 – Sweeds" lang="sv" hreflang="sv" data-title="Tröghetsmoment" data-language-autonym="Svenska" data-language-local-name="Sweeds" class="interlanguage-link-target"><span>Svenska</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-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 – Tadjiks" lang="tg" hreflang="tg" data-title="Моменти инерсия" data-language-autonym="Тоҷикӣ" data-language-local-name="Tadjiks" class="interlanguage-link-target"><span>Тоҷикӣ</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-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 – Turks" lang="tr" hreflang="tr" data-title="Eylemsizlik momenti" data-language-autonym="Türkçe" data-language-local-name="Turks" class="interlanguage-link-target"><span>Türkçe</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 – Tataars" lang="tt" hreflang="tt" data-title="İnertsiä momentı" data-language-autonym="Татарча / tatarça" data-language-local-name="Tataars" class="interlanguage-link-target"><span>Татарча / tatarça</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 – Oekraïens" lang="uk" hreflang="uk" data-title="Момент інерції" data-language-autonym="Українська" data-language-local-name="Oekraïens" 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 – Oerdoe" lang="ur" hreflang="ur" data-title="جمود کا معیار اثر" data-language-autonym="اردو" data-language-local-name="Oerdoe" class="interlanguage-link-target"><span>اردو</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 – Oezbeeks" lang="uz" hreflang="uz" data-title="Inersiya momenti" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</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 – Viëtnamees" lang="vi" hreflang="vi" data-title="Mô men quán tính" data-language-autonym="Tiếng Việt" data-language-local-name="Viëtnamees" 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-Sjinees" lang="wuu" hreflang="wuu" data-title="转动惯量" data-language-autonym="吴语" data-language-local-name="Wu-Sjinees" class="interlanguage-link-target"><span>吴语</span></a></li> <li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://zh.wikipedia.org/wiki/%25E8%25BD%2589%25E5%258B%2595%25E6%2585%25A3%25E9%2587%258F" title="轉動慣量 – Chinees" lang="zh" hreflang="zh" data-title="轉動慣量" data-language-autonym="中文" data-language-local-name="Chinees" class="interlanguage-link-target"><span>中文</span></a></li> <li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://zh-yue.wikipedia.org/wiki/%25E6%2585%25A3%25E6%2580%25A7%25E7%259F%25A9" title="慣性矩 – Kantonees" lang="yue" hreflang="yue" data-title="慣性矩" data-language-autonym="粵語" data-language-local-name="Kantonees" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> </section> </div> <div class="minerva-footer-logo"> <img src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" alt="Wikipedia" width="120" height="18" style="width: 7.5em; height: 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