# Is there an intuitional way to tell which physical quantities are angular frequency and which are frequency?

Such as the natural linewidth is defined to be angular frequency, while the absolute frequency of laser is frequency. By far I haven't found a good way not to learn it by roting. Would anyone be willing to share with me your thoughts if you have a better way?

• No, there in no intuitional way to tell. You have to know. Usually you will know because the word "angular" will be included to modify the word "frequency," but in speaking, or loose writing, people may forget. You can also tell by looking at a function, e.g., in $\sin(At)$, where $t$ is time then $A$ is an angular frequency, but, e.g., in $\sin(2\pi B t)$, where $t$ is time then $B$ is a [] frequency, not an angular frequency.
– hft
Jul 27, 2023 at 17:38
• P.S. "roting" is not a word that native English speakers ever use (at least in American English). In fact, very few native English speakers ever even use the word "rote" in current-day English.
– hft
Jul 27, 2023 at 17:39
• It's the choice of whoever is writing the expression. A common convention is that $f$ is cyclic frequency and $\omega$ is angular frequency, but don't count on it. Jul 27, 2023 at 18:13
• Angular frequency is frequency too. Every periodic function has a frequency, which simply is the reciprocal of its period. If you're talking about a periodic function of displacement in mm, then the frequency is reported as "per mm." If it's a periodic function of rotation in radians, then the frequency unit is "per radian." If it's a function of time measured in seconds, then the frequency unit is "per second." They're all "frequency." There's nothing special about "per second" beyond the fact that you probably hear it more often than the others. Jul 27, 2023 at 18:46

Frequency is frequency. You can say that a particle executing SHM in a cycle which repeats once per second has a frequency of 1 Hz. Or you can say that the displacement of the particle at time $$t$$ is $$A\sin(2 \pi t)$$, in which case you have assigned it a phase angle $$\theta = 2 \pi t$$ and you can say that its angular frequency in phase space is $$1$$ Hz. Although I think it would be more common to say that its angular velocity in phase space is $$2 \pi$$ radians per second.