The diameter of a flywheel is $1 \mathrm{~m}$. It has a mass of $20 \mathrm{~kg}$. It is rotating about its…

The diameter of a flywheel is $1 \mathrm{~m}$. It has a mass of $20 \mathrm{~kg}$. It is rotating about its axis with a speed of 120 rotations in one minute. Its angular momentum in $\mathrm{kg}-\mathrm{m}^2 / \mathrm{s}$ is
  1. $13.4$
  2. $31.4$
  3. $41.4$
  4. $43.4$

Solution

$\begin{aligned} & r=\frac{1}{2} \mathrm{~m}=0.5 \mathrm{~m}, m=20 \mathrm{~kg}, \\ & n=120 \text { rotation per minute, } \\ &=2 \text { rotation per sec. } \\ & \text { Angular momentum } L=I \omega \\ &=\frac{M r^2}{2} 2 \pi n=\frac{20 \times(0.5)^2}{2} \times 2 \times 3.14 \times 2 \\ &=5 \times 3.14 \times 2=31.4 \mathrm{~kg}-\mathrm{m}^2 / \mathrm{s}\end{aligned}$

Asked in: AP EAMCET 2002

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