The formula ωf = ωi + αt is derived from the definition of angular acceleration, which is the rate of change of angular velocity (ω) with respect to time (t). In other words, angular acceleration is the amount by which the angular velocity changes in a given time interval. Mathematically, angular acceleration (α) is defined as:

α = (ωf - ωi) / t

Rearranging this formula, we get:

ωf - ωi = αt

Adding ωi to both sides, we get:

ωf = ωi + αt

Therefore, ωf = ωi + αt is the equation that relates the final angular velocity (ωf) of an object to its initial angular velocity (ωi), angular acceleration (α), and the time interval (t) over which the acceleration occurs.
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