Sum of Translational and Angular Forces

[James Brady]

Hello, I'm trying to figure out the free body diagrams for the inverted pendulum problem and I'm having trouble figuring out the one equation:
$Psin\theta + Ncos\theta - mgsin\theta = ml\ddot{\theta} + m\ddot{x}cos\theta$

I've never really seen a mixed sum of forces equation before where some terms affect the angular acceleration of the rod and other terms affect the translational acceleration, so I'm not sure how to read this. Specifically, can anyone tell me:

• Should I just treat this as a decoupled equation, as in the P and N terms only affect the translational acceleration and the mg*sin(theta) terms only affects the angular acceleration?
• Why is there a cosine term next to the acceleration term on the right?

Basically, can you explain this equation to me Barney Style? I'd appreciate it.

 

[James Brady]

I had my physics major brother in law explain it to me. All is well now.