Sum of Translational and Angular Forces

AI Thread Summary
The discussion focuses on understanding the equation for the inverted pendulum problem, particularly the mixed sum of forces involving translational and angular accelerations. The user seeks clarification on whether to treat the equation as decoupled, with specific terms affecting either translational or angular acceleration. They also inquire about the presence of a cosine term in relation to the acceleration on the right side of the equation. The conversation highlights the complexities of analyzing forces in systems where both translational and angular motions are present. Overall, the user gains clarity on the equation with assistance from their brother-in-law.
James Brady
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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.
 
I had my physics major brother in law explain it to me. All is well now.
 

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