Solve the following :


A wheel rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. Find the angular acceleration and the angular velocity at the end of five seconds.


$\omega_{0}=0 ; \mathrm{t}=4 \mathrm{sec} ; \quad \theta=50$ rev $=100 \pi \frac{r a d}{\sec }$

Using, $\theta=\omega_{0} t+\frac{1}{2} \alpha t^{2}$

$\alpha=8 \pi^{\frac{r a d}{s e c^{2}}}$ or $\alpha=4 \pi \pi^{\frac{r e v}{s^{2}}}$

Using, $\omega=\omega_{0}+\alpha t$

$\omega=40 \pi \pi^{\frac{r a d}{s e c}}$ or $\omega=20 \frac{r e v}{\sec }$

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