Question:
A body rotates about a fixed axis with an angular acceleration of one radian/second/second. Through what angle does it rotate during the time in which its angular velocity increases from $5 \mathrm{rad} / \mathrm{s}$ to $15 \mathrm{rad} / \mathrm{s}$.
Solution:
$\omega_{0}=5 \mathrm{rad} / \mathrm{s} ; \omega=15 \mathrm{rad} / \mathrm{sec} ; \alpha=1 \mathrm{rad} / \mathrm{sec}^{2}$
Substituting values in,
$\omega^{2}=\omega_{0}^{2}+2 \alpha \theta$
$\theta=100 \mathrm{rad}$