A fan is rotating with an angular speed of 30 | vedclass

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(B) Initial angular speed $\omega_0 = 300 	ext{ rpm} = \frac{300 	imes 2\pi}{60} 	ext{ rad/s} = 10\pi 	ext{ rad/s}$.Final angular speed $\omega =

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$200$

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(B) Initial angular speed $\omega_0 = 300 	ext{ rpm} = \frac{300 	imes 2\pi}{60} 	ext{ rad/s} = 10\pi 	ext{ rad/s}$.Final angular speed $\omega = 0 	ext{ rad/s}$.Time taken $t = 80 	ext{ s}$.Using the equation of motion $\omega = \omega_0 + \alpha t$,we find the angular deceleration $\alpha$:$0 = 10\pi + \alpha(80) \Rightarrow \alpha = -\frac{10\pi}{80} = -\frac{\pi}{8} 	ext{ rad/s}^2$.The total angular displacement $	heta$ is given by $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$:$	heta = (10\pi)(80) + \frac{1}{2} \left(-\frac{\pi}{8}ight) (80)^2 = 800\pi - \frac{\pi}{16} (6400) = 800\pi - 400\pi = 400\pi 	ext{ rad}$.The number of revolutions $n$ is given by $n = \frac{	heta}{2\pi}$:$n = \frac{400\pi}{2\pi} = 200$.

$A$ fan is rotating with an angular speed of $300 \text{ rpm}$. The fan is switched off,and it takes $80 \text{ s}$ to come to rest. Assuming constant angular deceleration,the number of revolutions made by the fan before it comes to rest is:

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