Question

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad $s^{-1}$. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

Answer 1

Mass of the cylinder, m = 20 kg
Angular speed, $\omega =100rad{s}^{-1}$
Radius of the cylinder, r = 0.25 m
The moment of inertia of the solid cylinder:
$I=\frac{m{r}^2}{2}=\frac{1}{2}\times 20\times (0.25{)}^2=0.625kg{m}^2$
$\therefore$ Kinetic energy $=\frac{1}{2}I{\omega }^2=\frac{1}{2}\times 0.625\times (100{)}^2=3125J$
$\therefore$ Angular momentum, $L=I\omega =0.625\times 100=62.5Js$