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

Rajasthan 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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