Question

A fan is rotating with angular velocity $100rev/sec$. Then it is switched off. It takes $5$ minutes to stop. Find the value of angular retardation.

• A. $\frac{1}{3}rev/se{c}^2$
• B. $\frac{1}{2}rev/se{c}^2$
• C. $\frac{2}{3}rev/se{c}^2$
• D. $\frac{1}{6}rev/se{c}^2$

Answer 1

The correct option is A $\frac{1}{3}rev/se{c}^2$

Answer is A.
In this case, the initial angular velocity of the fan is ${\omega }_0=0$ and the final angular velocity of the fan is $\omega =100rev/sec$.
The value of angular retardation is calculated as follows.
$\omega ={\omega }_0+\alpha t\Rightarrow 0=100-\alpha (5\times 60)\Rightarrow \alpha =\frac{1}{3}\frac{rev}{se{c}^2}$.
Hence, the value of angular retardation is $\frac{1}{3}\frac{rev}{{sec}^2}$.