This formula is derived using the definitions of angular velocity and angular acceleration. Angular velocity is defined as the change in angle (θ) over time (t), or ω = θ/t. Angular acceleration is defined as the change in angular velocity over time, or α = (ωf - ωi) / t.

If we rearrange the equation for angular acceleration, we get:

α = (ωf - ωi) / t

Multiplying both sides by t, we get:

αt = ωf - ωi

Adding ωi to both sides, we get:

ωf = ωi + αt

This is the formula we use to calculate the final angular velocity of a rotating object starting from an initial angular velocity and undergoing an angular acceleration for a certain time.
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