Question

If the equation for the angular displacement of a particle moving on a circular path is given by $\theta =2t^3+0.5$, where $\theta$ is in radians and $t$ in seconds, then the angular velocity of the particle at $2\text{s}$ is

• A. $8\text{rad/s}$
• B. $12\text{rad/s}$
• C. $24\text{rad/s}$
• D. $36\text{rad/s}$

Answer 1

The correct option is C $24\text{rad/s}$

Given that $\theta =2t^3+0.5$
We know that,
Angular velocity $\omega =\frac{d\theta }{dt}$
Therefore, at $t=2s$.
$\omega =6t^2=6\times (2{)}^2=24\text{rad/s}$
Hence, the correct answer is option (c).