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  4. A particle performs uniform circular motion with an angular momentum L. If the frequency of particles motion is doubled and its KE is halved. the angular momentum becomes

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Q. A particle performs uniform circular motion with an angular momentum L. If the frequency of particles motion is doubled and its KE is halved. the angular momentum becomes

JamiaJamia 2006

Solution:

The angular momentum is measure for the amount of torque that has been applied over time to the object. For a particle with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as $ L=I\omega $ ....(i) where I is moment of inertia of particle and $ \omega $ the angular velocity. Also, $ K=\frac{1}{2}I{{\omega }^{2}} $ ...(ii) where K is kinetic energy of rotation. From Eqs. (i) and (ii), we get $ L=\frac{2K}{{{\omega }^{2}}}\omega =\frac{2K}{\omega } $ $ L=\frac{2(K/2)}{2\omega }=\frac{1}{4}\left( \frac{2K}{\omega } \right)=\frac{L}{4} $ Note: In a closed system angular momentum is constant.