Question

Two thin discs each of mass $M$ and radius $R$ are placed at either end of a rod of mass $m$, length $l$ and radius $2r$. Find the moment of inertia of the system about an axis passing through the centre of rod and perpendicular to its length.

Answer 1

$I=I_{Rod}+2I_{Disc}$

$I=(\frac{m{L}^2}{12}+\frac{m(2r{)}^2}{4})+$ $2(\frac{M{R}^2}{4}+\underset{Parallelaxis}{\underset{}{M{\left(\frac{L}{2}\right)}^2}})$

$I=\frac{m{L}^2}{12}+\frac{4m{r}^2}{4}+\frac{2M{R}^2}{4}+\frac{2M{L}^2}{4}$

$I=\frac{m{L}^2}{12}+m{r}^2+\frac{M{R}^2}{2}+\frac{M{L}^2}{2}$ $kg{m}^2$