Solve the following :

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,

$\omega^{2}=\omega_{0}^{2}+2 \alpha \theta$

$\omega=4 \pi \sqrt{5} \mathrm{rad} / \mathrm{sec}$

$\omega=2^{\sqrt{5}} \mathrm{rev} / \mathrm{sec}$

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