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Systems of Particles and Rotational Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSystems of Particles and Rotational Motion3 Marks
Question
A solid cylinder of mass $20kg$ rotates about its axis with angular speed $100rads^{-1}$. The radius of the cylinder is $0.25m$. 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?
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Answer

Mass of the cylinder, m = 20kg Angular speed, $\omega= 100\text{rads}^{-1}$ Radius of the cylinder, r= 0.25m The moment of inertia of the solid cylinder, $\text{I}=\frac{\text{mr}^2}{2}$
$=\frac{1}{2}\times20\times(0.25)^2$
$=0.625\text{kgm}^2$
$\therefore$ Kinetic energy $=\frac{1}{2}\text{I}\omega^2$
$=\frac{1}{2}\times6.25\times100^2=3125\text{J}$
$\therefore$ Angular momentum, $\text{L} = \text{I}\omega = 6.25\times100 = 62.5\text{Js}$

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