I'm currently writing my own physics simulation engine for some practice with physics since I plan on taking it as my major along with computer science and would like to be ahead of the curve. Plus I'm just plain interested in it. I've read through some papers such as

Chris Hecker's article for 2D physics and

this paper from an online SIGGRAPH course.

I've come across a major problem in the Hecker article however.... unless I read it wrong, he doesn't take it account where the force is applied when determining the linear force on an object. My intuition says that if I hit an object square in the middle, all of the force will be directed into the linear acceleration of the object. If I hit it on the corner however, more of the force will be put into the angular momentum and less in the linear direction. Is this the right way to think of it?

This is an excerpt from the article on 2D rotation:

1. Calculate the CM and the moment of inertia at the CM.

2. Set the body’s initial position, orientation, and linear and angular velocities.

3. Figure out all of the forces on the body, including their points of application.

**4. Sum all the forces and divide by the total mass to find the CM’s linear acceleration**
5. For each force, form the perpdot product from the CM to the point of force application and add the value into the total torque at the CM (Eq. 11).

Step 4 seems completely wrong to me. You should see where the linear force acts on the object relative to the center of mass and then go from there.

So my question is how exactly are linear and angular force related. Do they both add up to equal the total force imparted on the object?

P.S. Easy on the notation, I'm not too knowledgeable on all of the symbols