Meaning and unit of frequency in Laplace (Fourier) transform
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