When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many more rotations will it make before coming to rest?

Question

Aicharya · Accepted Answer

For, angular velocity falls to half when the fan is switched off,
$\begin{aligned} & \omega_f^2-\omega_i^2=2 a \theta \\ & \Rightarrow\left(\frac{\omega_f}{2}\right)^2-\omega_i^2=2 a \times 36 \times 2 \pi \quad ... (1) \end{aligned}$ For, angular velocity falls to zero when the fan is switched off,
$\rightarrow \mathrm{O}^2-\omega^2=2 \mathrm{a} \times \mathrm{N} \times 2 \pi$ ...(2)
we get, $N=48$
So, the fan will make $48-36=12$ more rotations before it stops.

When a ceiling fan is switched off, its angular velocity falls to half while it makes 36 rotations. How many…

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