Question:
Find the angular velocity of a body rotating with an acceleration of $2 \mathrm{rev} / \mathrm{s}^{2}$ as it completes the $5^{\text {th }}$ revolution after the start.
Solution:
$\omega_{0}=0, \alpha=2 \frac{r e v}{s^{2}}=2 \times 2 \pi=4 \pi \frac{r a d}{s^{2}}$
$\theta=5 \mathrm{rev}=5 \times 2 \pi \mathrm{rad}=10 \pi \mathrm{rad}$
Substituting values in,
$\omega^{2}=\omega_{0}^{2}+2 \alpha \theta$
$\omega=4 \pi \sqrt{5} \mathrm{rad} / \mathrm{sec}$
$\omega=2^{\sqrt{5}} \mathrm{rev} / \mathrm{sec}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.