When a ceiling fan is switched off its ang

By using equation ${\omega ^2} = \omega _0^2 - 2\alpha \theta $

${\left( {\frac{{{\omega _0}}}{2}} \right)^2} = \omega _0^2 - 2\alpha (2\pi n)$

$⇒$ $\alpha = \frac{3}{4}\frac{{\omega _0^2}}{{4\pi \times 36}}$, $(n = 36)$..$(i)$

Now let fan completes total $n'$ revolution from the starting to come to rest

$0 = \omega _0^2 - 2\alpha (2\pi n')$ $⇒$ $n' = \frac{{\omega _0^2}}{{4\alpha \pi }}$

substituting the value of   from equation $(i)$

$n' = \frac{{\omega _0^2}}{{4\pi }}\frac{{4 \times 4\pi \times 36}}{{3\omega _0^2}} = 48$ revolution

Number of rotation $= 48 -36 = 12$