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== LaTeX Equation Array == | |||
<tex> | <tex> | ||
T | \begin{eqnarray} | ||
\int_{A}r\left(\frac{r}{R}\tau_{max}\right)dA | \nonumber T & = & \int_{A}r(\tau{dA})= | ||
& = & \frac{\tau_{max}}{R}\int_{A}r^{2}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^{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 & = & | ||
\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}\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} | = \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}\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\frac{\pi{R}^4}{2} = | ||
\frac{\tau_{max}}{R}\times{J} | \frac{\tau_{max}}{R}\times{J} | ||
\end{eqnarray} | |||
</tex> | </tex> | ||
Revision as of 02:04, 16 February 2009
x > y
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>