Angular frequency

Beginner

Rate of phase advance.

Key relationω = 2πf

ω = 2πf = 2π/T in rad/s; for a spring ω = √(k/m), for a pendulum √(g/L). It's not the same as the speed of the particle.

Worked example

f = 2 Hz means ω = 12.6 rad/s.

Common mistake

Don't mix Hz and rad/s.

In more detail

The angular frequency ω = 2πf is measured in radians per second and appears in the equations of motion. It determines how quickly the phase advances.

Engineers use angular frequency to predict resonance in machines.
Electronics uses angular frequency in filter and circuit design.
A radio station broadcasts at a frequency of 100 MHz, which is an angular frequency of about 6.3 × 10⁸ radians per second.

How does ω relate to f?

ω equals 2π times f.

What is the period in terms of ω?

T equals 2π divided by ω.

Is angular frequency the same as frequency?

No. Angular frequency is 2π times the frequency and is measured in radians per second.