Question

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

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

Answer 1

The correct option is C $24rad/s$

Given

$\theta =2t^3+0.5$

Differentiating w.r.t t, we get

$\frac{d\theta }{dt}=6t^2$

$\omega =6t^2$

At t=2 sec

$\omega =6(2{)}^2=24rad/sec$