Question

The power (P) is supplied to rotating body having moment of inertia 'I' and angular acceleration '\(α\)'. Its instantaneous angular velocity is

• A. \(\frac{I}{Pα}\)
• B. \(\frac{α}{PI}\)
• C. \(\frac{Pα}{I}\)
• D. \(\frac{P}{Iα}\)

Hint:

P = torque times omega and torque = I alpha.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
For a rotating body, power is torque times angular velocity: \(P=\tau\omega\). Torque is \(\tau=I\alpha\).

Step 2: Combine:
\[ P=I\alpha\,\omega \]

Step 3: Solve for omega:
\[ \omega=\frac{P}{I\alpha} \]

Step 4: Choose:
Option (D). Options (A), (B) and (C) have the wrong dimensions. For example \(\tfrac{I}{P\alpha}\) does not reduce to rad/s.

Final Answer:
Angular velocity is P divided by I alpha. \[ \boxed{\omega=\frac{P}{I\alpha}} \]