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Display information for equation id:math.2006.76 on revision:2006
* Page found: Kinetische Energie und Trägheitstensor (eq math.2006.76)
(force rerendering)Occurrences on the following pages:
Hash: a50f04545f26a618793b1f2c62afc929
TeX (original user input):
\begin{align}
& J=\frac{8}{3}\pi \int_{0}^{R}{dr{{r}^{4}}\rho (r)}=\frac{2M}{{{R}^{3}}}\int_{0}^{R}{dr{{r}^{4}}} \\
& J=\frac{2}{5}M{{R}^{2}} \\
\end{align}
TeX (checked):
{\begin{aligned}&J={\frac {8}{3}}\pi \int _{0}^{R}{dr{{r}^{4}}\rho (r)}={\frac {2M}{{R}^{3}}}\int _{0}^{R}{dr{{r}^{4}}}\\&J={\frac {2}{5}}M{{R}^{2}}\\\end{aligned}}
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MathML (1.878 KB / 416 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>J</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>8</mn></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow><mi>π</mi><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>r</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup><mi>ρ</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>M</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mfrac></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>r</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></msup></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>J</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mn>5</mn></mrow></mfrac></mrow><mi>M</mi><msup><mi>R</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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