Question

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. $2{\theta }_2$

Answer 1

The correct option is D $2{\theta }_2$

Angle turned by the body $\theta ={\theta }_0+{\theta }_{1}t+{\theta }_2{t}^2$
Angular velocity
$\omega =\frac{d\theta }{dt}$
$=\frac{d}{dt}({\theta }_0+{\theta }_{1}t+{\theta }_2{t}^2)$
$={\theta }_1+2{\theta }_{2}t$
Angular acceleration
$\alpha =\frac{dw}{dt}$
$=\frac{d}{dt}({\theta }_1+2{\theta }_{2}t)$
$=2{\theta }_2$