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Angular acceleration in terms of angular velocity

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I've been working on problems that deal with pendulums and I've noticed that a few of my answers require me to find the angular velocity, frequency, period of a pendulum. I managed to get the answer right every time, but there's a step that I didn't understand, namely converting angular acceleration to angular velocity by what seems to be using this relationship:

[itex]\alpha=\omega^2[/itex]

Where in the heck does this come from? :confused: The book kind of skips this step in the examples and doesn't prove it at all, even though it proves just about every other equation it mentions.

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