Answer
$18\dfrac {rad}{s^{2}}$
Work Step by Step
To find angular acceleration, we need to find the angular velocity first. So the angular velocity of point is:
$w\left( t\right) =\dfrac {\partial \left( \theta \right) }{\partial t}=\dfrac {\partial }{\partial t}\left( 4t-3t^{2}+t^{3}\right) =4+3t^{2}-6t........(1)$
The angular acceleration at any given time is:
$\alpha \left( t\right) =\dfrac {\partial w}{\partial t}=\dfrac {\partial }{\partial t}\left( 4-6t+3t ^{2}\right)=6t-6 ..................(2)$
So using (2) and $t=4s$, we get:
$\alpha \left( 4\right) =6\times 4-6=18\dfrac {rad}{s^{2}}$
