Question:
If \( I \), \( E \) and \( L \) are the moment of inertia, rotational kinetic energy, and angular momentum respectively, then:
If \( I \), \( E \) and \( L \) are the moment of inertia, rotational kinetic energy, and angular momentum respectively, then:
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The moment of inertia is related to the rotational kinetic energy and angular momentum by \( I = \frac{E}{L} \).
Updated On: Apr 18, 2026
- \( I = \frac{E}{L} \)
- \( 2E = \frac{I}{L} \)
- \( L = \sqrt{2EI} \)
- \( E = L = \frac{L}{I} \)
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The Correct Option is A
Solution and Explanation
The rotational kinetic energy \( E \) is related to the moment of inertia \( I \) and angular velocity \( \omega \) by the equation:
\[
E = \frac{1}{2} I \omega^2
\]
The angular momentum \( L \) is related to the moment of inertia and angular velocity by the equation:
\[
L = I \omega
\]
From these two equations, we can solve for \( \omega \) in terms of \( L \) and \( I \):
\[
\omega = \frac{L}{I}
\]
Substitute this value of \( \omega \) into the equation for \( E \):
\[
E = \frac{1}{2} I \left( \frac{L}{I} \right)^2 = \frac{L^2}{2I}
\]
Now, solving for \( I \):
\[
I = \frac{E}{L}
\]
Thus, the correct relation is \( I = \frac{E}{L} \), which corresponds to option (A).
Final Answer: (A) \( I = \frac{E}{L} \)
Final Answer: (A) \( I = \frac{E}{L} \)
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