Question

A disc is having an initial angular velocity of $4\text{rad/sec}$ and angular acceleration of $8{\text{rad/sec}}^2$. Find the angle rotated (in radian) by disc in $3\text{sec}$.

• A. $48\text{rad}$
• B. $36\text{rad}$
• C. $12\text{rad}$
• D. $24\text{rad}$

Answer 1

The correct option is A $48\text{rad}$

Given, Initial angular speed,
${\omega }_o=4\text{rad/sec}$
Angular acceleration,
$\alpha =8{\text{rad/sec}}^2$, $t=3\text{sec}$
Using the equation of the angular displacement,
$\theta ={\omega }_{o}t+\frac{1}{2}\times \alpha t^2$
$=4\times 3+\frac{1}{2}\times 8\times 3^2$
$=48\text{rad}$