A flywheel is accelerated uniformly from rest | vedclass

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Question

(B) Given that the flywheel starts from rest,the initial angular velocity $\omega_0 = 0$.Using the equation of rotational motion $	heta = \omega_0 t

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(B) Given that the flywheel starts from rest,the initial angular velocity $\omega_0 = 0$.Using the equation of rotational motion $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$,where $\alpha$ is the angular acceleration.For the first second $(t = 1 \, s)$,the angle rotated is $	heta_1 = 5 \, rad$:$5 = 0(1) + \frac{1}{2} \alpha (1)^2 \implies \alpha = 10 \, rad/s^2$.Now,we find the total angle rotated in the first two seconds $(t = 2 \, s)$:$	heta_2 = 0(2) + \frac{1}{2} (10) (2)^2 = 5 	imes 4 = 20 \, rad$.The angle rotated in the next second (from $t = 1$ to $t = 2$) is the difference between the total angle in $2 \, s$ and the angle in $1 \, s$:$\Delta 	heta = 	heta_2 - 	heta_1 = 20 - 5 = 15 \, rad$.

$A$ flywheel is accelerated uniformly from rest and rotates through $5 \, rad$ in the first second. The angle rotated by the flywheel in the next second will be ......... $rad$.

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