The change in angular position with time, the angular analogue of linear velocity. It is a vector, having both magnitude and direction. In introductory mechanics we will almost always deal with cases of angular velocity about a single axis of rotation, so that the angular velocity is confined to one dimension.
Mathematical Definition
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\begin
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[\omega = \frac{d{\theta}}
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]\end
Because we will always deal with one-dimensional angular velocity (more specifically, the angular velocity about one chosen axis of rotation in any given problem), we have dropped the vector arrows from the definition.