A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s ^{-1} radius of c

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6.System of Particles and Rotational Motion

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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?

Option A

Option B

Option C

Option D

Solution

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, $L=I \omega$

$=6.25 \times 100$

$=62.5 Js$

Standard 11

Physics

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(IIT-2019)