$A$ 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?

(N/A) Given:
Mass of the cylinder,$m = 20 \; kg$
Angular speed,$\omega = 100 \; rad \; s^{-1}$
Radius of the cylinder,$r = 0.25 \; m$
The moment of inertia $(I)$ of a solid cylinder about its axis is given by:
$I = \frac{1}{2} m r^2$
$I = \frac{1}{2} \times 20 \times (0.25)^2 = 10 \times 0.0625 = 0.625 \; kg \; m^2$
$1$. Rotational Kinetic Energy $(K)$:
$K = \frac{1}{2} I \omega^2$
$K = \frac{1}{2} \times 0.625 \times (100)^2$
$K = 0.5 \times 0.625 \times 10000 = 3125 \; J$
$2$. Angular Momentum $(L)$:
$L = I \omega$
$L = 0.625 \times 100 = 62.5 \; kg \; m^2 \; s^{-1}$ (or $J \; s$)