When no external torque acts on a rotating system,
- angular momentum of the system is not conserved
- its rotational kinetic energy is conserved
- its rotational kinetic energy is independent of moment of inertia
its rotational kinetic energy is inversely proportional to moment of inertia
its rotational kinetic energy is directly proportional to moment of inertia
The Correct Option is D
Solution and Explanation
When no external torque acts on a rotating system, the system undergoes conservation of angular momentum. This means that the angular momentum of the system remains constant.
The angular momentum \( L \) of a rotating body is given by: \[ L = I \omega \] Where: - \( I \) is the moment of inertia, - \( \omega \) is the angular velocity. When there is no external torque, angular momentum is conserved, i.e., \( L \) remains constant. The rotational kinetic energy \( K \) of a rotating body is given by: \[ K = \frac{1}{2} I \omega^2 \] Since \( L = I \omega \), we can express \( \omega \) in terms of \( L \) and \( I \): \[ \omega = \frac{L}{I} \] Substituting this into the equation for \( K \): \[ K = \frac{1}{2} I \left( \frac{L}{I} \right)^2 = \frac{L^2}{2I} \] From this, we can see that the rotational kinetic energy \( K \) is inversely proportional to the moment of inertia \( I \) when angular momentum \( L \) is conserved. Thus, the correct statement is: \[ \text{Rotational kinetic energy is inversely proportional to moment of inertia.} \]
Correct Answer:
Correct Answer: (D) its rotational kinetic energy is inversely proportional to moment of inertia
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