Question

With usual notations for a rigid body in rotational motion about a fixed axis, its

• A. kinetic energy is \(I\omega^{2}\)
• B. angular momentum is \(I\omega\)
• C. work done is \(\tau^{2}\omega^{2}\)
• D. power is \(\tau \omega^{2}\)
• E. angular velocity is \(\frac{d\omega}{dt}\)

Hint:

\(L = I\omega\) is the rotational analogue of linear momentum \(p = mv\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
For rotational motion, angular momentum \(L = I\omega\).

Step 2: Detailed Explanation:
1. Kinetic energy = \(\frac{1}{2}I\omega^2\), not \(I\omega^2\).
2. Angular momentum = \(I\omega\) — correct.
3. Work done = \(\tau \theta\), not \(\tau^2\omega^2\).
4. Power = \(\tau \omega\), not \(\tau \omega^2\).
5. Angular velocity = \(\omega\), \(\frac{d\omega}{dt}\) is angular acceleration.

Step 3: Final Answer:
Angular momentum is \(I\omega\).