Question

(1) A ceiling fan having moment of inertia 2 kg m´attains its maximum frequency of in 21 seconds. Calculate its power rating. ​

Answer 1

Answer:

Given

I = Moment of inertia = 2\ \text{kg m}^22 kg m

2

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

30

π

=2π rad/s

t = Time taken = 2\pi\ \text{s}2π s

To find

Power rating of fan

Solution

\begin{gathered}\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\end{gathered}

ω

f

=ω

i

+αθ

⇒α=

t

ω

f

−ω

i

⇒α=

2π

2π−0

⇒α=1 rad/s

2

Power is given by

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

P=Iαω

⇒P=2×1×2π=

⇒P=4π=12.56 W