A flywheel rotates with a uniform angular acc | vedclass

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(B) Given: Initial angular velocity $\omega_{0} = 20\pi \, rad/s$,final angular velocity $\omega = 40\pi \, rad/s$,and time $t = 10 \, s$.Using the eq

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$150$

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(B) Given: Initial angular velocity $\omega_{0} = 20\pi \, rad/s$,final angular velocity $\omega = 40\pi \, rad/s$,and time $t = 10 \, s$.Using the equation of motion $\omega = \omega_{0} + \alpha t$,we find the angular acceleration $\alpha$:$40\pi = 20\pi + \alpha(10) \Rightarrow 20\pi = 10\alpha \Rightarrow \alpha = 2\pi \, rad/s^{2}$.Now,calculate the total angular displacement $	heta$ using $	heta = \omega_{0}t + \frac{1}{2}\alpha t^{2}$:$	heta = (20\pi)(10) + \frac{1}{2}(2\pi)(10)^{2} = 200\pi + 100\pi = 300\pi \, rad$.Since one rotation is equal to $2\pi \, rad$,the number of rotations $n$ is given by $n = \frac{	heta}{2\pi}$:$n = \frac{300\pi}{2\pi} = 150$ rotations.

$A$ flywheel rotates with a uniform angular acceleration. Its angular velocity increases from $20\pi \, rad/s$ to $40\pi \, rad/s$ in $10 \, s$. How many rotations did it make in this period?

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