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Thread: Center of mass

  1. #1
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    Center of mass

    https://imgur.com/a/KZOxs

    Can someone let me know why I got this wrong?
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  2. #2
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    Re: Center of mass

    $\begin{align*}
    &M = \displaystyle \int_0^{\frac{\pi}{2}}~2\sin(2x)~dx = \\ \\

    &\left . -\cos(2x) \right |_0^{\frac \pi 2} = \\ \\

    &-(-1 - 1) = 2

    \end{align*}$

    $\begin{align*}
    &M_x = \displaystyle \int_0^{\frac \pi 2}\int_0^{2\sin(2x)}~y~dy~dx = \\ \\

    &\displaystyle \int_0^{\frac \pi 2}~\left(\left .\dfrac{y^2}{2}~\right|_0^{2\sin(2x)}\right) ~dx = \\ \\

    &\displaystyle \int_0^{\frac \pi 2}~2\sin^2(2x)~dx = \dfrac{\pi}{2}

    \end{align*}$

    $\overline{y} = \dfrac{M_x}{M} = \dfrac{\frac \pi 2}{2} = \dfrac \pi 4$
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