How Do I Calculate Motor Specs for an Inverted Pendulum Project?

[Ele38]

Hi to everyone.
This is my second dissussion in the forum (it does not exist a presentation section, right? ), and I need your help for my Diploma project.
Since I am studying Electronics&Telecommunications, my idea about that project is to build an inverted pendulum and tomake a PID controller able to stabylize the pendulum.
The base of the project is a Microchip's AN, here's the link http://ww1.microchip.com/downloads/en/AppNotes/00964A.pdf
Unlike Microchip engineers, I want to make a PID controller with operational amplifier, I think that is a better project fo my senior year.
Here is my problem.
Reading the AN, there is written that we need a motor which must be able, at least, to accelerate as fast as the pendulum can fall.
I have no idea about how to calculate the motor's specs (torque, rpm, ... ) I have a 120 rpm motor, but I do no think that will be ok for the project.
Does someone can help me? I would need formulas, since I have mathematics at the oral test for the diploma, it could be good to have something to discuss (even if there is a lot of mathematics in the PID :D )
Thank you very much ;)

 

[Ele38]

I thought about something today.
What is really important to me? Torque or rpm? I think torque, since is in N*m I can calculate the Force that the motor applies to the cart and using the formula F=m*a I am able to calculate the acceleration of the cart.
Am I mad or it can work?