The mass moment of inertia $I$ measures resistance to angular acceleration. For a body rotating about an axis, $I=\int r^{2}dm$ where $r$ is the perpendicular distance from the axis to the mass element. For a uniform slender rod of mass $m$ and length $L$, about an axis through one end (perpendicular to the rod): $I=\frac{1}{3}m{L}^2$. About the center: $I_G=\frac{1}{12}m{L}^2$. The parallel-axis theorem relates $I_O=I_G+m{d}^2$.

Notation: $I$ = mass moment of inertia, $m$ = mass, $L$ = length, $I_G$ = about center of mass, $d$ = distance between parallel axes.

A uniform slender rod has mass 6 kg and length 2 m. The axis of rotation is perpendicular to the rod and passes through one end of the rod.

Find:

1. The mass moment of inertia of the rod about this axis.

Mass moment of inertia about the end: $I_O=8\text{kg}\cdot {\text{m}}^2$.