Angular displacement

You can use angles to describe position around a circle. There can be angular displacement, just from ${\theta }_f-{\theta }_i$. Direction is usually counterclockwise = positive. Just like math quadrants.

Angular Velocity

The angular velocity, denoted by $\omega$, is angular displacement overtime, $\frac{\Delta \theta }{\Delta t}=\omega$.

Angular acceleration

The change in angular velocity over time, $\frac{{\omega }_f-{\omega }_i}{\Delta t}$.

All instantaneous quantities for velocity and acceleration are obtained through taking the limit as $\Delta t$ approaches zero.

The linear velocity is $\frac{\Delta l}{\Delta t}$. Of course, $\Delta l=\theta r$ as with definitions of Radians. So the instantaneous linear velocity at any point is $\frac{\Delta \theta r}{\Delta t}$, or $r\omega$. Notice how the larger $r$ is, the higher the linear velocity. Points farther along the axis travel faster.

Connecting to Kinematics, divide everything by $r$, you will get all the same formulas.