A fan starts from rest and makes 10 revolutio | vedclass

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(C) The angle covered in the first $3$ seconds is $	heta_{3s} = 10 	imes 2\pi = 20\pi 	ext{ rad}$.Using the kinematic equation $	heta = \omega_0 t

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$30$

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(C) The angle covered in the first $3$ seconds is $	heta_{3s} = 10 	imes 2\pi = 20\pi 	ext{ rad}$.Using the kinematic equation $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$,where initial angular velocity $\omega_0 = 0$:$20\pi = 0 + \frac{1}{2} \alpha (3)^2 \Rightarrow 20\pi = \frac{9}{2} \alpha \Rightarrow \alpha = \frac{40\pi}{9} 	ext{ rad/s}^2$.Now,the total angle covered in $6$ seconds ($t = 6$ s) is:$	heta_{6s} = \frac{1}{2} \alpha (6)^2 = \frac{1}{2} 	imes \left( \frac{40\pi}{9} ight) 	imes 36 = 80\pi 	ext{ rad}$.The angle covered in the next $3$ seconds (from $t = 3$ s to $t = 6$ s) is:$\Delta 	heta = 	heta_{6s} - 	heta_{3s} = 80\pi - 20\pi = 60\pi 	ext{ rad}$.The number of revolutions in the next $3$ seconds is $n = \frac{\Delta 	heta}{2\pi} = \frac{60\pi}{2\pi} = 30$.

$A$ fan starts from rest and makes $10$ revolutions in the first $3$ seconds. Assuming constant angular acceleration,how many revolutions will it make in the next $3$ seconds?

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