Question

When no external torque acts on a rotating system,

• A. angular momentum of the system is not conserved
• B. its rotational kinetic energy is conserved
• C. its rotational kinetic energy is independent of moment of inertia
• D. its rotational kinetic energy is inversely proportional to moment of inertia
• E. its rotational kinetic energy is directly proportional to moment of inertia

Answer 1

The Correct Option is D

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