# Part A Suppose a uniform slender rod has length L and mass m. The moment of inertia of the rod about about an axis that is perpendicular to the rod and that

Part A Suppose a uniform slender rod has length L and mass m. The moment of inertia of the rod about about an axis that is perpendicular to the rod and that

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unessodopunsep
a) Using property given,
$I={I}_{cm}+M{d}^{2}$
Here, $d=\frac{L}{2}$
Hence,
$I=\frac{M{L}^{2}}{12}+\frac{M{L}^{2}}{4}=\frac{M{L}^{2}}{3}$
b) Using shift property of moment of inertia
$I=\frac{M{\alpha }^{2}}{6}+\frac{M{\alpha }^{2}}{2}=\frac{2M{\alpha }^{2}}{3}$