Question:
A body is rotating with angular momentum L. If $ I $ is its moment of inertia about the axis of rotation, its kinetic energy of rotation is
A body is rotating with angular momentum L. If $ I $ is its moment of inertia about the axis of rotation, its kinetic energy of rotation is
Updated On: Jul 29, 2022
- $ \frac{1}{2}I{{L}^{2}} $
- $ \frac{1}{2}IL $
- $ \frac{1}{2}{{I}^{2}}L $
- $ \frac{1}{2}\frac{{{L}^{2}}}{I} $
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The Correct Option is D
Solution and Explanation
We know that $ L=I\omega $ Kinetic energy of a body with angular momentum $ KE=\frac{1}{2}I{{\omega }^{2}} $ $ KE=\frac{1}{2}\times I\times {{\left( \frac{L}{I} \right)}^{2}} $ $ KE=\frac{{{L}^{2}}}{2I} $
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Concepts Used:
Kinetic energy
Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.
