Answer:
[tex]\theta = 144 radian[/tex]
Explanation:
As we know that angular acceleration is defined as rate of change in angular velocity
so here we can write
[tex]\frac{d\omega}{dt} = \alpha[/tex]
Now we will have
[tex]\int d\omega =\int \alpha dt[/tex]
[tex]\omega - \omega_0 = \int (10 + 6t) dt[/tex]
here initial angular speed is ZERO as it start from rest
[tex]\omega = 10t + 3t^2[/tex]
now we can say that rate of change in angular position is known as angular velocity
So here we will have
[tex]\theta = \int \omega dt[/tex]
[tex]\theta = \int^4_0 (10t + 3t^2) dt[/tex]
[tex]\theta = (5t^2 + t^3)_0^4[/tex]
[tex]\theta = 144 radian[/tex]
