Question

Four thin rods each of mass $m$ and length $l$ are joined to make a square. Find moment of inertia of all the four rods about any side of the square.

Answer 1

For rod $AB$ or $DC$, MOI along $AD$ is $\frac{m{l}^2}{3}$ for each and for $BC$ along $AD$ is $m{c}^2$.

Thus, combined $MOI{)}_{AD}=\frac{2m{l}^2}{3}+m{l}^2$

or $I_{AD}=\frac{5m{l}^2}{3}$