Question

A fan starts rotating with an angular acceleration $2{\text{rad/s}}^2$. After it accelerates for $5\text{s}$, for next $5\text{s}$ it rotated with constant velocity & then deaccelerates for next $10\text{s}$ & stops. Find the total number of rotations.

• A. $\frac{255}{\pi }$
• B. $\frac{60}{\pi }$
• C. $\frac{125}{2\pi }$
• D. $\frac{120}{\pi }$

Answer 1

The correct option is C $\frac{125}{2\pi }$


$\omega ={\omega }_0+\alpha t_1$

$=0+2\times 5$

After $5\text{sec},$ $\omega =10\text{rad/s}$

Total angular displacement = area enclosed by the trapezium $=\frac{1}{2}\times 10\times (5+20)$

$=5\times 25$

$=125\text{rad}$

So, no. of rotations $\text{n}=\frac{\text{angular displacement}}{2\pi }=\frac{125}{2\pi }$


Hence, option $\left(A\right)$ is correct.