Angular velocity can change just as linear velocity can. Angular acceleration measures that change.

Over a finite time interval,

$$\bar\alpha=\frac{\Delta\omega}{\Delta t}.$$

Sign

The sign of angular acceleration depends on the chosen positive rotation direction. It does not by itself say whether the object is speeding up.

If $\omega$ and $\alpha$ have the same sign, the magnitude of angular velocity increases. If they have opposite signs, it decreases.

Constant angular acceleration

When $\alpha$ is constant,

$$\omega=\omega_0+\alpha t,$$

and

$$\theta=\theta_0+\omega_0t+\frac12\alpha t^2.$$

These are the rotational counterparts of the constant-acceleration equations for linear motion.

Linear acceleration of a point

For a point at distance $r$ from the axis, changing angular speed produces tangential acceleration of magnitude

$$a_t=r|\alpha|.$$

Rotation can also produce radial acceleration when the direction of velocity changes, even if angular speed is constant.