# For a physical pendulum, why do you use an angular coordinate system when the centre of mass translates too?

I am trying to understand why you can use $$F=ma$$ for a simple pendulum, yet need the rotational equivalent for a physical pendulum. I understand it is because the rigid body can rotate too, whereas you don't consider that for a simple pendulum and consider just the mass under translational motion. I just don't understand why you don't have to consider translational motion with the physical pendulum? My understanding was kinetic energy is the sum of the translational kinetic energy of the centre of mass and rotational kinetic energy where it is rotating about the centre of mass? I'm not sure how to use this information though for a physical pendulum when it is rotating about a different axis?

• The formula $\tau= I_{support}\alpha$ (which uses an angular coordinate system) can also be used on a simple pendulum. You will have to assume a point mass "rotating" about the hinge. – harshit54 Aug 2 at 21:48

With any extended object such as a physical pendulum, you are considering not the force on a single particle but on all of the particle (atoms, molecules, whatever) that make up the object: right off the bat, you're considering the positions of $$10^\text{something}$$ particles.