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  4. Circular disc of mass 2 kg and radius 1 m is rotating about an axis perpendicular to its plane and passing through its centre of mass with a rotational kinetic energy of 8 J. The angular momentum in (J-s) is

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Q. Circular disc of mass 2 kg and radius 1 m is rotating about an axis perpendicular to its plane and passing through its centre of mass with a rotational kinetic energy of 8 J. The angular momentum in (J-s) is

EAMCETEAMCET 2008System of Particles and Rotational Motion

Solution:

Rotational kinetic energy $ =\frac{1}{2}I{{\omega }^{2}}=8\,J $ $ \Rightarrow $ $ \frac{1}{2}\times \frac{1}{2}m{{r}^{2}}{{\omega }^{2}}=8 $ or $ \frac{1}{4}\times 2\times {{(1)}^{2}}{{\omega }^{2}}=8 $ or $ {{\omega }^{2}}=16 $ or $ \omega =4\,rad/s $ Angular momentum, $ L=I\omega $ $ =\frac{1}{2}m{{r}^{2}}\omega $ $ =\frac{1}{2}\times 2\times {{(1)}^{2}}\times 4 $ $ =4\,J-s $