Frequency or Angular Frequency

I am doing study on electromagnetism and Drude model is applied recently in my simulation. I am quite confused about the exact meaning of the terms in the expression of the dielectric constant in Drude model.

I have tried with the case of gold and here is what I got from my calculations:

One the one hand, the $$\omega$$ within in the denominator should be interpreted as the angular frequency with rad/s as the unit. On the other hand, the plasma frequency in the numerate and the damping coefficient in the denominator should be interpreted as the frequency with unit Hz.

By interpreted I mean just substitute in the value of the quantity while it is with that particular unit

But can the angular frequency just be added with frequency given their different units?

• Both frequency and angular frequency are measure in Hz. You have to be told if the variables are angular or not, although there is a very very strong convention that $\omega$ is angular frequency, and a somewhat strong convention that $f$ is frequency. Often it doesn't matter, as the expression is the ratio of frequencies. (Assuming the author didn't do something stupid.) But you can't add variables if one is $f$ and the other $\omega$. May 8, 2020 at 12:52
• @garyp It is killing me. I have substitute the value of $\omega$ when it is in rad/s and the values of $\omega_p$ and $\Gamma$ when they are in 1/s to get the right dielectric constant of for example gold, which is well established.
– cxz
May 8, 2020 at 13:41
They are related simply by a factor of $$2\pi$$,
$$\omega = 2\pi\nu$$
where $$\nu$$ is in Hz and $$\omega$$ is rads/s.