For which $n$ would an object with a non-zero rotation fall to the center of this field?

$$\alpha >0\\ V(r) = \frac{\alpha}{r^n}$$

(Apparently it should never touch the center if it has non-zero rotation and $n=1$). I am totally stumped, as I cant see why the order should change whether or not it falls into the center. Any ideas/explanations would be greatly appreciated.