A wheel of radius 1.5 m rotates with a const | vedclass

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(A) Given: Radius $r = 1.5 \ m$,angular acceleration $\alpha = 10 \ rad/s^2$,initial angular speed $\omega_0 = (\frac{60}{\pi}) \ rpm$,time $t = 2.0 \

Vedclass · Accepted Answer

$22 \ rad/s, 24 \ rad$

Vedclass · Answer

(A) Given: Radius $r = 1.5 \ m$,angular acceleration $\alpha = 10 \ rad/s^2$,initial angular speed $\omega_0 = (\frac{60}{\pi}) \ rpm$,time $t = 2.0 \ s$.First,convert $\omega_0$ to $rad/s$:$\omega_0 = \frac{60}{\pi} 	imes \frac{2\pi}{60} = 2 \ rad/s$.Using the first equation of rotational motion,$\omega = \omega_0 + \alpha t$:$\omega = 2 + (10 	imes 2) = 2 + 20 = 22 \ rad/s$.Using the second equation of rotational motion for angular displacement,$	heta = \omega_0 t + \frac{1}{2} \alpha t^2$:$	heta = (2 	imes 2) + \frac{1}{2} 	imes 10 	imes (2)^2 = 4 + (5 	imes 4) = 4 + 20 = 24 \ rad$.

$A$ wheel of radius $1.5 \ m$ rotates with a constant angular acceleration of $10 \ rad/s^2$. Its initial angular speed is $(\frac{60}{\pi}) \ rpm$. What will be its angular speed and angular displacement at $t = 2.0 \ s$?

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