When a ceiling fan is switched on,it makes 10 | vedclass

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(C) The fan starts from rest,so initial angular velocity $\omega_0 = 0$.Using the equation of rotational motion: $	heta = \omega_0 t + \frac{1}{2} \a

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$30$

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(C) The fan starts from rest,so initial angular velocity $\omega_0 = 0$.Using the equation of rotational motion: $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$.For the first $t_1 = 3 \, s$,the number of rotations $n_1 = 10$,so the angular displacement $	heta_1 = 2 \pi n_1 = 20 \pi \, rad$.$20 \pi = 0 + \frac{1}{2} \alpha (3)^2 \implies 20 \pi = \frac{9}{2} \alpha \implies \alpha = \frac{40 \pi}{9} \, rad/s^2$.For the total time $t_2 = 3 + 3 = 6 \, s$,let the total number of rotations be $n_2$.$	heta_2 = 2 \pi n_2 = 0 + \frac{1}{2} \alpha (6)^2 = 18 \alpha$.Substituting $\alpha = \frac{40 \pi}{9}$:$2 \pi n_2 = 18 	imes \frac{40 \pi}{9} = 80 \pi$.$n_2 = 40$ rotations.The number of rotations in the next $3 \, s$ is $n_2 - n_1 = 40 - 10 = 30$ rotations.

When a ceiling fan is switched on,it makes $10$ rotations in the first $3 \, s$. How many rotations will it make in the next $3 \, s$ (Assume uniform angular acceleration)?

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