# Is there a fixed orientation of center of mass axis about which all unconstrained rigid bodies rotate?

I just learned that an unconstrained rigid body always rotates about its center of mass. But there could be many axes that could pass through the center of mass.

For example, let's consider a rod lying on a table which is given an impulse at one of its ends, from intuition we could say that the rod would rotate about an axis passing through the center of mass which is perpendicular to the table (The axis for which moment of inertia of the rod is $$\frac{ML^2}{12}$$ if the rod is uniform). But then the rod could've rotated about a different axis passing through the center of mass.

So my question is, among all such axes that pass through the center of mass does there always exist a definite orientation of the axis about which all unconstrained rigid bodies would rotate for a given scenario (such as all rigid bodies lying on a table, all freely falling bodies, etc)? If so, why does it always have to be in such an orientation?