Question

The angular velocity of a particle moving in a circle of radius $50\text{cm}$ is increased in $5\text{min}$ from $100$ revolutions per minute to $400$ revolutions per minute.
Find its angular acceleration in ${\text{rad/s}}^2$

Answer 1

Using the $1st$ equation of motion for circular motion, we get
${\omega }_f={\omega }_i+\alpha t$
$\Rightarrow 400=100+\alpha \left(5\right)$
$\Rightarrow 300=5\alpha$
$\Rightarrow \alpha =\frac{300}{5}{\text{rev/min}}^2$
$=\frac{300\times 2\pi }{5\times 60\times 60}$

$=\frac{\pi }{30}=0.10{\text{rad/s}}^2$