Question

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

• A. 13.4
• B. 31.4
• C. 41.4
• D. 43.4

Answer 1

Answer: (B)

Here,
Diameter of a flywheel, $D = 1\, m$
Radius of the flywheel, $R=\frac{D}{2}=\frac{1}{2}m$
Mass of the flywheel, $M = 20\, kg$
Angular speed of rotation,
$\omega=120\,rpm=\frac{2\pi\times120}{60}rad\,s^{-1}=4\pi\,rad\,s^{-1}$
Moment of inertia of the flywheel about its axis,
$I=\frac{1}{2}MR^{2}=\frac{1}{2}\left(20\,kg\right) \left(\frac{1}{2}m\right)^{2}$
$=2.5\,kg\,m^{2}$
Angular momentum, $L = I\omega$
$=\left(2.5\right)\left(4\pi\right)$
$=10\pi$
$=31.4\,kg\,m^{2}\,s^{-1}$