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      <text>15.2.2.4 y coord of COM of lamina by vertical strips</text>
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      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p></p>
<p>In this exercise we use the same tall and narrow rectangles as in the previous exercise, but we now consider the moment about the \(x\)-axis in order to find \(\bar{y}\).&nbsp;&nbsp;</p>
<figure class="HELM_figure"><img src="@@PLUGINFILE@@/15-2-2-3-fig2.svg" alt="" width="300" height="272" class="img-responsive atto_image_button_text-bottom"><br></figure>

<ol class="HELM_parts">

    <li>Referring to the figure again, the centre of mass of the rectangular slice must lie half way along its length, that is, its \(y\)-coordinate is \(\dfrac{y}{2}=\dfrac{x}{2}\). Assume that all the mass of the slice, \(x \rho \delta x\), acts at this
        point, the moment about the \(x\)-axis is:<br>[[input:ans0]][[validation:ans0]]&nbsp;[[feedback:prt0]]<br>Enter <code> rho</code> for \(\rho\).<br>
        <p><br></p>
    </li>
    <p></p>
    <li>Adding contributions from all slices gives the sum and letting&nbsp;\(\delta x \to 0\) we obtain the integral:
        <p></p>
        <p>\( \displaystyle{\int_{x=0}^{2}}\) [[input:ans1]]\(\textrm{d}x\) [[validation:ans1]]&nbsp;[[feedback:prt1]]</p>
    </li>
    <li>Evaluate the above integral.
        <p>[[input:ans2]] [[validation:ans2]]&nbsp;[[feedback:prt2]]</p>
    </li>
    <li>Similar to the previous exercise the moment of the total mass about the \(x\)-axis is \(2 \rho \bar{y}\). Setting this equal to the value in part (c) determine \(\bar{y}\).
        <p></p>
        <p><span style="font-size: 0.9375rem;">\(\bar{y}=\)[[input:ans3]] [[validation:ans3]]&nbsp;[[feedback:prt3]]</span><br></p>
    </li>
</ol>]]></text>
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<file name="15.2.2 Stage 2.png" path="/" encoding="base64">[encoded data, 52032 characters]</file>
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      <text><![CDATA[<ol class="HELM_parts">
    <li>
        <p>\(\displaystyle {@ta0@}\)</p>
    </li>
    <li>
        <p>\(\displaystyle \int_{x=0}^{2} \frac{\rho y^2}{2} \textrm{d}x\)</p>
    </li>
    <li>
        <p>\({4 \rho}{3}\)</p>
    </li>
    <li>
        <p>\(2 \rho \bar{y} = \dfrac{4 \rho}{3} \) from which \(\bar{y} = \dfrac{2}{3}\). The coordinates of the centre of mass are \((\frac{4}{3}, \frac{2}{3})\).</p>
    </li>
</ol>]]></text>
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ta0:x^2*rho*deltax/2;
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ta2:(4*rho)/3;
ta3:2/3;
ta4:[4/3, 2/3]]]></text>
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