Question:

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

Updated On: Jul 5, 2022
  • 2 L
  • 4L
  • $\frac{L}{2}$
  • $\frac{L}{4}$
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The Correct Option is D

Solution and Explanation

$L=mvr=mr^2 \omega$ Also kinetic energy K =$\frac{1}{2}mv^2$ or $K=-\frac{1}{2}m(r \omega )^2$ $=\frac{1}{2}mr^2 \omega^2$ $K=\frac{1}{2}mr^2 \omega^2$ $K=\frac{1}{2}\frac{L}{\omega}\omega^2=\frac{L\omega}{2}$ $\Rightarrow L=\frac{2K}{\omega}$ hence $\omega '=2 \omega $ or $K'=\frac{1}{2}K$ hence $L'=\frac{2K'}{\omega'}=\frac{2\left(\frac{1}{2}K\right)}{2 \omega}=\frac{L}{4}$
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Concepts Used:

System of Particles and Rotational Motion

  1. The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
  2. The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
  3. The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.