Question

A body rotates about a fixed axis with an angular acceleration of one radian/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

Given

Angular acceleration of the body = \[\alpha = 1\text{ rad/s}^2\]

Initial angular velocity of the body = \[\omega_0 = 5\text{ rad/s}^2\]

Final angular velocity of the body = \[\omega = 15 rad/s\]

We know that:

\[\omega =  \omega_0  + \alpha t\] 

\[ \Rightarrow t = \frac{\left( \omega - \omega_0 \right)}{\alpha} = \frac{\left( 15 - 5 \right)}{1} = 10  s\] 

Also,

\[\theta =  \omega_0 t + \frac{1}{2}\alpha t^2 \] 

\[ \Rightarrow \theta = 5 \times 10 + \frac{1}{2} \times 1 \times 100\] 

\[\Rightarrow \theta = 50 + 50 = 100\text{ rad}\]