Meaning and unit of frequency in Laplace (Fourier) transform Imagine transfer function obtained by Laplace transform, for example:

$G(s) = \dfrac{1}{s+1}$

Now, I would like to do some frequency analysis, so I replace the $s$ with $\omega i$ (let's consider this operation valid for this example).

What is the unit of the $\omega$? So far what I have seen, the $\omega$ is noted as frequency or angular velocity. I asked my colleagues and I got various answers:


rad/sec
Hz
no unit


What is correct and why? Does it depend on real variable passed to transform (if somebody uses different variable than time)?
If you are dealing with the Laplace transform $G(s)$ of a time domain signal $g(t)$ and its evaluation on the imaginary axis to get the Fourier transform $G(j\omega)$ (assuming it exists) then the unit of your frequency $\omega$ is radians per second assuming the unit of the time was seconds. 

It's relation to cyclic frequency is : $$\omega = 2 \pi f$$ where $f$ is the frequency in Hz (cycles per second).

On the other hand if the initial function was like $g(x)$ where $x$ was a spatial variable with unit of meters, then the transform domain frequency unit will be in radians per meter where its relation to space-frequency is still the same with $\omega = 2 \pi f$ where $f$ will have the unit of cycles per meter