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 rad/s to 15 rad/s.

Answer 1

$\alpha =1{\text{rad/s}}^2,{\omega }_0=5\text{rad/s},$ $\omega =15\text{rad/s},$

$\therefore \omega ={\omega }_0+\text{at}$

$\Rightarrow t=\frac{(\omega -{\omega }_0)}{\alpha }$

$=\frac{(15-5)}{1}=10\text{sec}$

$\text{Also,}\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

$=5\times 10+\frac{1}{2}\times 1\times 100$

$=50+50=100\text{rad}$