Question

A ceiling fan having moment of inertia 2 kgm2 attains maximum frequency of 60 rpm in 2π second’s,  calculate it’s power rating .  ​

Answer 1

Given

I = Moment of inertia = $2\ \text{kg m}^2$

$f$ = Frequency of rotation = 60 rpm = $60\times \dfrac{\pi}{30}=2\pi\ \text{rad/s}$

t = Time taken = $2\pi\ \text{s}$

To find

Power rating of fan

Solution

$\omega_f=\omega_i+\alpha\theta\\\Rightarrow \alpha=\dfrac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\dfrac{2\pi-0}{2\pi}\\\Rightarrow \alpha=1\ \text{rad/s}^2$

Power is given by

$P=I\alpha \omega\\\Rightarrow P=2\times 1\times 2\pi=\\\Rightarrow P=4\pi=12.56\ \text{W}$

The power rating of the fan is 13 W.

Answer 2

Answer:

the power rating of a fan is 30 W

Explanation:

hope it's helpful