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  4. The diameter of a flywheel is 1 m . It has a mass of 20 kg . It is rotating about its axis with a speed of 120 rotations in one minute. Its angular momentum in kg m 2 s-1 is

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Q. The diameter of a flywheel is $1\, m$ . It has a mass of $20\, kg$ . It is rotating about its axis with a speed of $120$ rotations in one minute. Its angular momentum in $kg\, m ^2\, s^{-1}$ is

System of Particles and Rotational Motion

Solution:

Here, $d=1\,m, v=120\, rpm , M=20\, Kg$
$r=\frac{d}{2}=\frac{1}{2} m=0.5\, m$
$ \omega=2 \pi v=\frac{2 \pi \times 120}{60}=4 \pi\, rad\, s^{-1}$
$\therefore L=I \omega=\frac{M r^2}{2} \omega=\frac{20 \times(0.5)^2 \times 4 \pi}{2}$
$=10 \times 0.25 \times 4 \times 3.14=31.4\, kg\, m^2\, s^{-1}$