Question

The angle turned by a body undergoing circular motion depends on time as $\theta ={\theta }_0+{\theta }_{1}t+2{\theta }_2{t}^2$. Then the angular acceleration of the body is

• A. $4{\theta }_1$
• B. $4{\theta }_2$
• C. $2{\theta }_1$
• D. $2{\theta }_2$

Answer 1

The correct option is B $4{\theta }_2$

We know that
$\omega =\frac{d\theta }{dt}=\frac{d({\theta }_0+{\theta }_{1}t+2{\theta }_2{t}^2)}{dt}={\theta }_1+4{\theta }_{2}t$


Angular acceleration $\alpha =\frac{d\omega }{dt}=\frac{d}{dt}({\theta }_1+4{\theta }_{2}t)$
$\alpha =4{\theta }_2$