Angular Frequency ω

In Figure (1), we reminded ourselves that a sinusoidal oscillation is equivalent to the sideways view of circular motion. If the vector on the left side of Figure (1) is rotating with an angular velocity ω radians per cycle, we get one rotation, one period T of the oscillation, when the angle θ = ωt goes from 0 at t = 0, to 2π at t = T. Thus at the end of one period, θ = ωT = 2π .

Figure 1: Definition of the function sin θ = sin(ω t).

Again we can avoid memorizing new formulas by using dimensions. We note that 2π is the number of radians in a full circle or cycle. Thus we will assign to it the dimensions

...........(1)

Then to find the formula, for example, for the wave's angular frequency ω in terms of the wave's period T, we have

...........(2)