Question

If $\theta$ depends on time $t$ in following way
$\theta =2t^2+3$ then find out the average angular velocity $\left(\Delta \omega \right)$ up to $3\text{sec}$ and angular velocity $\left(\omega \right)$ at $3\text{sec}$. $\left(\text{in rad/s}\right)$

• A. $6,12$
• B. $6,6$
• C. $8,12$
  
• D. $12,4$

Answer 1

The correct option is A $6,12$

$\Delta \omega =\frac{\text{Change in angular displacement}}{\text{Change in time}}=\frac{{\theta }_f-{\theta }_i}{t_2-t_1}$
${\theta }_f=2(3{)}^2+3=21\text{rad}$
${\theta }_i=2\left(0\right)+3=3\text{rad}$
So, $\Delta \omega =\frac{21-3}{3}=6\text{rad/sec}$
${\omega }_{\text{instantaneous}}=\frac{d\theta }{dt}=4t$
${\omega }_{t=3\text{sec}}=4\times 3=12\text{rad/sec}$

Hence option (a) is the correct answer.