A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is______.

Final angular velocity ${\omega }_i=2\pi f=\frac{2\pi \times 1800}{60}=60\pi rad/s$

Initial angular velocity  ${\omega }_f=\frac{2\pi \times 600}{60}=20\pi rad/s$

Using ${\omega }_f={\omega }_i+\alpha t$

$60\pi =20\pi +\alpha \left(10\right)$

Angular acceleration, $\alpha =4\pi rad/s^2$

We have,  $\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

$\theta =20\pi \left(10\right)+\frac{1}{2}\left(4\pi \right){\left(10\right)}^2=400\pi$ radian.

Number of rotations $n=\frac{\theta }{2\pi }=\frac{400\pi }{2\pi }=200$