In nature there are many examples of this. A satellite revolves in circular motion around the earth. One specific type of circular motion is uniform circular motion. That is a particle that moves along a circumference with a constant velocity, the direction in which it moves varies continually because it is tangent to the circumference.
Period + frequency
-Period: the time that a particle at a certain point needs to complete a complete revolution along a circumference. The period is written as T and is measured in seconds. That is to say that if a particle in uniform circular motion is at a certain point at a determined instant in time, after a period it will be at the same location.
-Frequency: the number of revolutions a particle completes in a given time. Is measured in Hertz (Hz).
Angular velocity is the relation between the angular distance and the time to travel the distance. If a particle moves in uniform circular motion while travelling along the circumference it forms an arc. The radius tha extends from the particle points to the centre gives an angle.
The angle "theta" is directly proportional to the arc travelled of the particle. Therefore the velocity of the particle depends on the angle of the radius instead of the arc lenght. In uniform circular motion angular velocity is constant.