# Rotating and Shifting image doesn't change FFT2

I have an image and its fourier transform. When I rotate it, its fourier transform rotates too, but I can't figure it out. Why does this happen? On the other hand, when I shift the image, its fourier transform doesn't change. As I know, time shifting means frequency shifting. Am Iwrong?

$$f(x) \Rightarrow F(w) \\ f(x-a) \Rightarrow e^{-j2\pi wa} F(w)$$