Question

If the equation for the 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 the angular velocity of the particle after $2s$ from its start is

• A. $8rad/s$
• B. $12rad/s$
• C. $24rad/s$
• D. $36rad/s$

Answer 1

The correct option is C $24rad/s$

Angular displacement of the particle $\theta \left(t\right)=2t^3+0.5$ radians

$\therefore$ Angular velocity $w=\frac{d\left[\theta \right(t\left)\right]}{dt}=6t^2$ rad/s

Angular velocity at $t=2$ s $w{|}_{t=2}=6\times 2^2=24$ $rad/s$