# 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

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