Circular Motion #9

The angular velocity of a particle performing circular motion is $\omega \ \hat{i}$ .

$\omega$ varies with time according to the following equation:

$\omega = \frac{1}{ 4}t^{2} - \sin \left( \pi t + \frac{\pi}{3} \right)$

If the magnitude of angular acceleration of the particle, $\alpha$ , at $t = 3$ can be written $a + b\pi$ for some rational numbers $a$ and $b$ , what is $a + b$ ?

---

This problem is part of the set - Circular Motion Practice