Let dθ be the angular displacement made by the particle in time dt, then the angular velocity of the particle is ω = dθ/dt. Its unit is rad s-1 and the dimensional formula is T-1.
For one complete revolution, the angle swept by the radius vector is 360° or 2π radians. If T is the time taken for one complete revolution, known as period, then the angular velocity of the particle is: ω = θ/t = 2π/t.
If the particle makes n revolutions per second, then, ω = 2π (1/T) = 2π n where n = 1/T is the frequency of revolution.