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Problem 09.101 - Mohr's circle for the orientation of the principle axes and the principal moments of inertia
10 points
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Using Mohr's circle, determine for the area indicated the orientation of the principal centroidal axes and the corresponding values of the moments of inertia. Given that $\overline{I}_{x}=2.28 \text{ in}^{4}$, $\overline{I}_{y}=4.87 \text{ in}^{4}$, and $\overline{I}_{xy}=-1.77 \text{ in}^{4}$.
0.25 in.
0.980 in.
y
0.487 in.
x
C
2 in.
L3 $\times$ 2 $\times$ $\frac{1}{4}$
0.25 in.
3 in.
The principal axes are obtained by rotating the xy axes through $\square^{\circ}$ about C. $\circlearrowright$
The maximum moment of inertia is $\square$ in$^{4}$. (Round the final answer to three decimal places.)
The minimum moment of inertia is $\square$ in$^{4}$. (Round the final answer to three decimal places.)