Question

Why do we use angular velocities for a particle having circular motion?

Answer 1

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Answer 2

Angular velocity for a single particle is often studied in introductory physics classes because it's easier than angular velocity of an extended body (that is, an object composed of many, possible infinitely many, "particles"). In real physics, the concept of angular velocity for point masses is really only useful in studying the motions of planets or particles in a system with more than one. Also, there is an analogous quantity called "spin" in quantum mechanics which behaves a lot like angular momentum, but it is completely different.
Angular velocity is very useful for rigid body problems.

Answer 3

@Herp_Derp Thank you.