The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its…
The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis passing through its mid-point and perpendicular to its length is $I_0$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
$I_0+M L^2 / 4$
$I_0+2 M L^2$
$I_0+M L^2$
$I_0+M L^2 / 2$
Solution
The theorem of parallel axis for moment of inertia.
$\begin{aligned}
& I=I_{\mathrm{CM}}+M h^2 \\
& I=I_0+M\left(\frac{L}{2}\right)^2
\end{aligned}$
$I=I_0+\frac{M L^2}{4}$
.