A disc rotating about its axis from rest,acqu | vedclass

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(D) Initial angular speed,$\omega_0 = 0 \, rad/s$. Final angular speed,$\omega = 100 \, rev/s = 100 	imes 2\pi \, rad/s = 200\pi \, rad/s$. Time,$t =

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$400$

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(D) Initial angular speed,$\omega_0 = 0 \, rad/s$. Final angular speed,$\omega = 100 \, rev/s = 100 	imes 2\pi \, rad/s = 200\pi \, rad/s$. Time,$t = 4 \, s$. Using the equation of rotational kinematics,$\omega = \omega_0 + \alpha t$: $200\pi = 0 + \alpha(4) \Rightarrow \alpha = 50\pi \, rad/s^2$. Now,the angle rotated $	heta$ is given by $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$: $	heta = 0(4) + \frac{1}{2} (50\pi) (4)^2$. $	heta = \frac{1}{2} 	imes 50\pi 	imes 16 = 400\pi \, rad$. Thus,the angle rotated is $400\pi$ radians.

$A$ disc rotating about its axis from rest,acquires the angular speed $100 \, rev/s$ in $4 \, s$. The angle rotated by it during these four seconds (in radian) is ...... $\pi$.

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