Model Treybuchet Arm: Moment of Inertia & DEs

[bassplayer142]

I am trying to model a treybuchet arm. What I'm looking to achieve is an equation that shows the acceleration of the arm where the object is released. I have been looking into moments of inertia for the arm itself but I get stuck considering that there is a heavy weight used as Pot energy to get the arm to swing. Deriving a moment of inertia equation for a pole is easier with equally distributed math. For that do I need differential Equations? Any help with the mathematical setup is appreciated.

If it is indeed differential equations does anyone know a good book or link that goes over using DEs in models. I have taken a class but you mostly just learn how to solve them, not how to set them up.

thanks

 

[DyslexicHobo]

As far as the moment of inertia goes, you should be able to break it up into multiple parts by using the parallel axis theorem (assuming that you can break it up into relatively simple shapes).

I can't really help you much with the dynamics portion, considering I barely passed that class last semester. >_<

 

[bassplayer142]

I never heard of the parallel axis theorem. Thanks for the help.

 

[DyslexicHobo]

No problem. The parallel axis theorem allows you to calculate the moment of inertia about any axis. If you take the moment of inertia of each component (in this case it would most likely be the arm and the weight) about the object's centroid you can then calculate the object's moment of inertia about the centroid. From there, I believe you can use the same calculations to find the moment about another axis.

You may want advice from someone a little more studied in the subject, because it's still kind of blurry to me. We only went over 2-3 problems involving the parallel axis theorem this semester and I didn't exactly pass that class with flying colors.