Question

The moment of inertia and rotational kinetic energy of a rigid body are 4 $kgm^2$ and 50 J respectively. The angular velocity of the body (in rad $s^{-1}$) is:

• A. 10
• B. 20
• C. 25
• D. 5
• E. 15

Hint:

This is the rotational analog of linear kinetic energy $K = \frac{1}{2} mv^2$, where $I$ replaces $m$ and $\omega$ replaces $v$.

Answer 1

The Correct Option is D

Step 1: Concept
Rotational Kinetic Energy $K_r = \frac{1}{2} I \omega^2$.

Step 2: Analysis
Given $K_r = 50\ J$ and $I = 4\ kgm^2$.

Step 3: Calculation
$50 = \frac{1}{2} (4) \omega^2 \implies 50 = 2 \omega^2$. $\omega^2 = 25 \implies \omega = 5\ rad\ s^{-1}$. Final Answer: (D)