Question

Determine the moment of Inertia of a uniform disc having mass M and radius R about an axis passing through centre & perpendicular to the plane, of the disc?

Answer 1

$I=\int d{I}_{ring}$
element - ring $dI=dm{r}^2$
$dm=\frac{M}{\pi R^2}2\pi rdr$ (here we have used the uniform mass distribution)

$\therefore I={\int }_0^R\frac{M}{\pi R^2}.\left(2\pi rdr\right).r^2$

$\Rightarrow I=\frac{M{R}^2}{2}$