Question

If the equation for the angular displacement of a particle moving on a circular path is given by $\left(\theta \right)=2t^3+0.5$, where $\theta$ is in radians and $t$ in seconds, then find the angular velocity of the particle after $2$ seconds from its start.

Answer 1

Angular displacement, $\theta =2t^3+0.5$

Angular velocity, $\omega =\frac{d\theta }{dt}$

$⟹\theta =6t^2$

At $t=2$ seconds

${\omega }_{t=2}=6\times 4=24$ $rad/s$