Question

A ceiling fan having moment of inertia 2 kg m2 attains it's maximum frequency 60 rpm in 2π seconds calculate its power rating

Answer 1

Power can be defined as the ratio of work done and the time taken to do the work.

$P = Work/Time$

• Now, work can be written as change in rotational kinetic energy.

$\implies P = \Delta KE/Time$

$\implies P = (\dfrac{1}{2}\: I\omega^{2})/Time$

• Convert $\omega$ from rpm to rad/sec unit and then put the values.

$\implies P = \{0.5 \times 2\times (60\times\dfrac{2\pi}{60})^{2}\}/2\pi$

$\implies P = 4\pi^{2}/2\pi$

$\implies P = 2\pi\:watt$

So, power rating is 2π watt.