Question

The angle turned by a body undergoing circular motion depends on time as $\theta = \theta_{o} + \theta_1t + \theta_2 t^2$ . Then the angular acceleration of the body is :

• A. $\theta_1$
• B. $\theta_2$
• C. $2 \theta_1$
• D. $2 \theta_2$

Answer 1

Answer: (D)

Angle turned by the body
$\theta=\theta_{0}+\theta_{1} t+\theta_{2} t^{2} $
$ =\frac{d \theta}{d t} $
$=\frac{d}{d t}\left(\theta_{0}+\theta_{1} t+\theta_{2} t^{2}\right)$
Angular velocity $=\theta_{1}+2 \theta_{2} t$
Angular acceleration $\alpha =\frac{d \omega}{d t} $
$=\frac{d}{d t}\left(\theta_{1}+2 \theta_{2} t\right) $
$=2 \theta_{2}$