Question

A body rotating with an angular speed of $600\text{rpm}$ is uniformly accelerated to $1800\text{rpm}$ in $10\text{sec}$. The number of rotations made in the process is ____

Answer 1

$\omega =\frac{2\pi N}{60}$

${\omega }_0=\frac{2\pi \times 600}{60}=20\pi \text{rad/s}$

${\omega }_f=\frac{2\pi \times 1800}{60}=60\pi \text{rad/s}$

Using equation,
${\omega }_f={\omega }_0+\alpha t$

$60\pi =20\pi +(\alpha \times 10)$

$\Rightarrow \alpha =4\pi {\text{rad/s}}^2$

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

$\theta =(20\pi \times 10)+\frac{1}{2}\times 4\pi \times {10}^2=400\pi \text{rad}$

So, number of rotations will be,
$n=\frac{400\pi }{2\pi }=200$