A rod of mass M and length L, initially standing, falls in such a way that the center of mass experiences only vertical motion. What is the moment of inertia of the rod? I picture the rod as having both translational and rotational motion since it's rotating about an axis through the CM which is moving vertically downward. I can also picture the rod as rotating about the end touching the surface, which is moving horizontally. Now, to find the moment of inertia, I need to pick a rotation axis. Which one of these axes should I pick?