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Angular Velocity

The angular v...

Question

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

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Solution

Using the $1 s t$ equation of motion for circular motion, we get
$ω_{f} = ω_{i} + α t$
$\Rightarrow 400 = 100 + α (5)$
$\Rightarrow 300 = 5 α$
$\Rightarrow α = \frac{300}{5} {rev/min}^{2}$
$= \frac{300 \times 2 π}{5 \times 60 \times 60}$

$= \frac{π}{30} = 0.10 {rad/s}^{2}$

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