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?
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?
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 of the solid cylinder:
$I=\frac{m r^{2}}{2}$
$=\frac{1}{2} \times 20 \times(0.25)^{2}$
$=0.625 kg m ^{2}$
$\therefore$ Kinetic energy $=\frac{1}{2} I \omega^{2}$
$=\frac{1}{2} \times 6.25 \times(100)^{2}=3125 J$
$\therefore$ Angular momentum, $L=I \omega$
$=6.25 \times 100$
$=62.5 Js$
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