Angular acceleration ($\vec{\alpha}$) describes the rate at which angular velocity changes. It serves as the rotational equivalent to linear acceleration, $\vec{a}$. If an object spins faster, slows down, or reverses its rotation, it experiences angular acceleration.

We define the average angular acceleration $\alpha_{\text{avg}}$ over a time interval $\Delta t$ as the change in angular velocity $\Delta \omega$ divided by the elapsed time.

In this expression, $\omega_f$ is the final angular velocity and $\omega_i$ is the known initial angular velocity.

Direction of Acceleration

Angular acceleration is a vector quantity whose sign matches the sign of $\Delta \omega$, the change in angular velocity, and not necessarily $\omega$, the direction of angular velocity.