Answer
$28\dfrac {rad}{s}$
Work Step by Step
Angular velocity of the point is:
$w\left( t\right) =\dfrac {\partial \theta }{\partial t}=\dfrac {\partial }{\partial t}\left( 4t-3t^{2}+t^{3}\right) =4-6t+3t^{2}$
So at time $t=4s$, we get:
$w\left( 4\right) =4-6t+3t^{2}=4-6\times 4+3\times 4^{2}=28\dfrac {rad}{s}$
