Question

Find the angular velocity of a body rotating with an acceleration of 2 rev/s${}^2$ as it completes the 5th revolution after the start.

Answer 1

$\theta =5\text{rev},\alpha =2{\text{rev/s}}^2,{\omega }_0=0,\omega =?$

${\omega }^2=\left(2\alpha \theta \right)$

$\Rightarrow \omega =\sqrt{(2\times 2\times 5)}$

$=2\sqrt{5}\text{rev/s}$

$\text{or}\theta =10\pi \text{rad}$

$\alpha =4\pi \text{rad/s}$

${\omega }_0=0$

$\omega$ = ?

$\omega =\sqrt{\left(2\alpha \theta \right)}$

$=(2\times 4\pi \times 10\pi )$

$=4\pi \sqrt{5}\text{rad/s}$

$=2\sqrt{5}\text{rev/s}$