Question:
A wheel is making revolutions about its axis with uniform angular acceleration. Starting from rest, it reaches $100 \mathrm{rev} / \mathrm{sec}$ in 4 seconds. Find the angular acceleration. Find the angle rotated during these four seconds.
Solution:
$\omega_{0}=0 ; \mathrm{t}=4 \mathrm{sec} ;$
$\omega=100 \frac{r e v}{\sec }=100 \times 2 \pi^{\frac{r a d}{s e c}}$
Using, $\omega=\omega_{0}+\alpha t$
$\alpha=50 \pi^{\frac{r a d}{r e c^{2}}}$ or
$\alpha=25 \pi^{\frac{r a d}{s e c^{2}}}$
Using, $\quad=\omega_{0} t+\frac{1}{2} \alpha t^{2}=400 \pi \mathrm{rad}$
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