## Engineering Mechanics: Statics & Dynamics (14th Edition)

$I=\frac{1}{2}ma^2$
We can find the required moment of inertia as follows: $I=\Sigma (I^{\prime}+md^2)$ $\implies I=3(\frac{ma^2}{12}+m(\frac{\sqrt{3}}{6}a)^2$ $\implies I=3(\frac{ma^2}{12}+m\frac{3}{36}a^2)$ $\implies I=\frac{1}{2}ma^2$