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I have a few questions about rigid body dynamics. I'm planning on making a 3D domino simulation similar to those domino rally games we all played as kids. I understand that the domino effect can get pretty complicated because it creates a chain of forces, but right now I'm having trouble simply understanding how a single domino acts.

Without much luck, I've searched all over google and this message board for several different phrases aboutrigid body dynamics,eccentric forces,advanced dynamics,linear and rotational motion, and so on. I found an answer to one of my questions in this thread, but I would like to ask it anyway so that I can clearly understand why that answer is right and how it applies to my problem.

As far as my physics education goes, I'm currently wrapping up a freshman physics course specifically about classical mechanics and specifically for scientists and engineers, so I'm not advanced but I should be able to understand direct explanations and equations. I've taken math through Cal II, Discrete Math, and Linear Algebra.

Here is my problem:

http://cj.sharpstudents.com/images/domino-FBD.gif [Broken]

I suppose you all would have preferred that I call the force, F, an impulse. It's an instantaneous force. Imagine thumping the domino with your middle finger.

Is my free-body diagram correct? I figured the static frictional force works in the same horizontal direction as F when F is above B, otherwise the domino would spin in place about the CoM.

Problem 1: http://cj.sharpstudents.com/images/domino-range.gif [Broken]

Is [tex]R_2[/tex] equal to [tex]R_1[/tex]?

Why?

My intution tells me that [tex]R_2[/tex] should be larger because more of the force goes into creating torque when F is applied at A than it does when F is applied near B, so less goes into creating linear acceleration. I'm guessing my big error here is thinking about the force asgoing intoanything. Why does the force create the same linear acceleration no matter how far it is applied from the CoM? Will you explain it to me in more detail than a single sentence that says something like "conservation of momentum"? I have a feeling I'm missing some simple, fundamental idea about how forces relate to torque and linear acceleration.

If [tex]R_2 = R_1[/tex], then consider the following image:

http://cj.sharpstudents.com/images/domino-eccentric.gif [Broken]

Assume there is no frictional or gravitational force in this example. Is the horizontal acceleration of the CoM equal to 0 regardless of where I put [tex]F_2[/tex] between B and C?

Problem 2: http://cj.sharpstudents.com/images/domino-rotationPivot.gif [Broken]

Here is my biggest problem, the one I cannot find an answer to anywhere.

Bysmall FI mean small relative to the mass. Imagine tapping a domino softly so that it falls over without point D sliding. Or imagine barely tapping a domino so that it starts to lean, but returns to its original vertical position. That is a small force here.

Bylarge FI mean large relative to the mass. Imagine thumping a domino so hard that the number of revolutions it completes appears to be a larger number than the horizontal displacement in centimeters. That's not a very relevant ratio, I know, but that is what I mean by a large force here.

Did I state that incorrectly? Should I talk about F being small and large relative to [tex]f_s[/tex]?

What I want to know is: does the axis of rotation change depending on the magnitude of F?

My intuition tells me that the domino rotates about D when the force is small, changing the moment arm to be the full height of the domino instead of half of the height and thus changing torque differently.

My intuition also tells me that the domino rotates about the CoM when the force is large.

How does the frictional force affect the axis of rotation?

Once again, I have a feeling that I'm missing some simple, fundamental idea.

Is it always rotating about the CoM and I'm confusing the CoM's linear acceleration with angular acceleration around another point? Once the angle from the vertical is larger than 0, does the gravitational force along with the rigid body's points of contact cause the CoM to accelerate towards the ground, giving me a false view of rotation? Does that mean that simulating it on a computer is more of an issue of collision detection than of another torque equation?

Since I gave these problems in two dimensions, I'm okay with an answer involving only two dimensions. I would like to fully understand how this all works in two dimensions before moving on to three dimensions anyway.

I know there are physics SDKs out there for programmers, but I'm more interested in learning than simply getting it done. This fall I will be turning this into a directed study project to go towards my undergraduate computer science degree, and I'm doing that so that I can learn as much physics, graphics programming, audio programming, and UI programming as I can before I finish my degree next year.

I will sincerely appreciate your effort if you give me reasonably detailed answers to my questions. Let me know if I forgot to mention any important information.

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# Dominoes: Translation and Rotation

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