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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