A wheel is rotating with angular velocity $2 rad/s$.It is subjected to a uniform angular acceleration $2.0rad/s^2.$What angular displacement does the wheel acquire after $10s$ ?

The wheel is in uniform angular acceleration, Hence-

$\omega ={\omega }_0+\alpha t\to$ Substituting the valves of ${\omega }_0,\alpha and t,$ we have

$\omega =2+2\times 10=22\raisebox{1ex}{$rad$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

$\theta ={\theta }_0+\frac{1}{2}\left({\omega }_0+\omega \right)t\to$Substituting ${\theta }_0=0$ for initial position, and ${\omega }_0$ from above equation, we have $\theta =0+\frac{1}{2}\left(2+22\right)10=120rad$.