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\int_{A}r\left(\frac{r}{R}\tau_{max}\right)dA \\
\int_{A}r\left(\frac{r}{R}\tau_{max}\right)dA \\
\nonumber & = & \frac{\tau_{max}}{R}\int_{A}r^{2}dA =
\nonumber & = & \frac{\tau_{max}}{R}\int_{A}r^{2}dA =
\frac{\tau_{max}}{R}\int_{0}^{2\pi}\!\int_{0}^{R}r^{2}r{dr}{d\phi}
\frac{\tau_{max}}{R}\int_{0}^{2\pi}\!\int_{0}^{R}r^{2}r{dr}{d\phi} =
=
\frac{\tau_{max}}{R}\int_{0}^{2\pi}\!\int_{0}^{R}r^{3}{dr}{d\phi} \\
\frac{\tau_{max}}{R}\int_{0}^{2\pi}\!\int_{0}^{R}r^{3}{dr}{d\phi} \\
\nonumber & = &
\nonumber & = &
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\frac{\tau_{max}}{R}\times{J}
\frac{\tau_{max}}{R}\times{J}
\end{eqnarray}
\end{eqnarray}
</tex>
</tex>



Revision as of 02:06, 16 February 2009

x > y

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LaTeX Equation Array

<tex> \begin{eqnarray} \nonumber T & = & \int_{A}r(\tau{dA})= \int_{A}r\left(\frac{r}{R}\tau_{max}\right)dA \\ \nonumber & = & \frac{\tau_{max}}{R}\int_{A}r^{2}dA = \frac{\tau_{max}}{R}\int_{0}^{2\pi}\!\int_{0}^{R}r^{2}r{dr}{d\phi} = \frac{\tau_{max}}{R}\int_{0}^{2\pi}\!\int_{0}^{R}r^{3}{dr}{d\phi} \\ \nonumber & = & \frac{\tau_{max}}{R}\int_{0}^{2\pi}\left[\frac{r^4}{4}\right]_{r=0}^{r=R}{d\phi} = \frac{\tau_{max}}{R}\int_{0}^{2\pi}\frac{R^4}{4}{d\phi} \\ \nonumber & = & \frac{\tau_{max}}{R}\left[\frac{R^4}{4}\phi\right]_{\phi=0}^{\phi=2\pi}

\frac{\tau_{max}}{R}\times\frac{\pi{R}^4}{2}

\frac{\tau_{max}}{R}\times{J} \end{eqnarray} </tex>