I'm trying to understand the dynamic equations for the cart pole system according to this control tutorial from the University of Michigan, where the angular acceleration equation can be written as
$(I+ml^2)\ddot{\theta}+mglsin(\theta)+ml\ddot{x}cos(\theta)=0$
I'm having trouble understanding what forces are represented separately by the terms $ml^2\ddot{\theta}$ and $I\ddot{\theta}$. Both seem to represent a moment force exerted by the mass of the pole, so they almost seem to represent exactly the same thing. My intuition tells me that I really only need the term $ml^2\ddot{\theta}$, but the fact that there is an additional $I\ddot{\theta}$ term suggests that my intuition is not accounting for some other force present in the system.
Any help to clarify and distinguish the meaning behind these two terms would be greately appreciated!