A body rotating with uniform angular accelera | vedclass

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(A) Given: Initial angular velocity $\omega_0 = 0 	ext{ rad/s}$ (since it starts from rest).Angular displacement $	heta = 100 \pi 	ext{ rad}$.Time

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(A) Given: Initial angular velocity $\omega_0 = 0 	ext{ rad/s}$ (since it starts from rest).Angular displacement $	heta = 100 \pi 	ext{ rad}$.Time $t = 5 	ext{ s}$.Using the second equation of rotational motion: $	heta = \omega_0 t + \frac{1}{2} \alpha t^2$.Substituting the values: $100 \pi = 0 + \frac{1}{2} \alpha (5)^2$.$100 \pi = \frac{25}{2} \alpha$.$\alpha = \frac{200 \pi}{25} = 8 \pi 	ext{ rad/s}^2$.Now,using the first equation of rotational motion: $\omega = \omega_0 + \alpha t$.$\omega = 0 + (8 \pi) 	imes 5 = 40 \pi 	ext{ rad/s}$.Thus,the angular speed at the end of $5 	ext{ s}$ is $40 \pi 	ext{ rad/s}$.

$A$ body rotating with uniform angular acceleration covers $100 \pi \text{ rad}$ in the first $5 \text{ s}$ after the start. Its angular speed at the end of $5 \text{ s}$ (in $\text{rad/s}$) is .........$\pi$.

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