Q. The angle turned by a body undergoing circular motion depends on time as $\theta = \theta_{0} +$ $\theta_{1}t + \theta_{2}t^{2}$. Then the angular acceleration of the body is
A) $\theta_{1}$
B) $\theta_{2}$
C) ${2\theta}_{1}$
D) ${2\theta}_{2}$
Explanation
(d) Angle turned by the body
$\theta = \theta_{0} + \theta_{1}t + \theta_{2}t^{2}$
Angular velocity $\omega = \frac{d\theta}{dt}$
$= \frac{d}{dt}(\theta_{0} + \theta_{1}t + \theta_{2}t)$
$= \theta_{1} + 2\theta_{2}t$
Angular acceleration $\alpha = \frac{d\omega}{dt}$
$= \frac{d}{dt}\left( \theta_{1} + 2\theta_{2}t \right)$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 2\theta_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.