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Inertia of a slender rod A slender rod of constant density lies along the line segment $\mathbf { r } ( t ) = t \mathbf { j } + ( 2 - 2 t ) \mathbf { k } , 0 \leq t \leq 1 ,$ in the $y z$ -plane. Find the moments of inertia of the rod about the three coordinate axes.

$\delta \sqrt{5}\left(\frac{t^{2}}{3}\right)_{0}^{1}=\frac{\sqrt{5}}{3} \delta$

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