# Translational and Rotational motion

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I'm trying to set up the physics for a 2D game involving spaceships. I've gotten stuck on modeling the combination of translation and rotation from a thrust. I've got no problem here: Where the thrust is pointed through the center of mass, or where the thrust is in opposite directions and equidistant from the center. But I'm not sure how to model that right case if engine A was turned off, for example. Obviously, there will be a combination of translation (since nothing is opposing it) and rotation, but how much of each? And where is this center of rotation? It doesn't seem like it'd be the center of mass anymore. The center of rotation is my main problem, as all the rotation/torque stuff in my physics book assumes a set point of rotation (like an axle or door hinge) But it's pretty easy to set up examples where I have no idea where it should be rotating around: Can someone explain, or point me in the right direction? I'm not really sure what I should be studying for this.

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You might take a look at this series of articles (a little way down the page, under physics articles).

I'm not a physics expert, so you should take anything I say with a grain of salt. But, I think unconstrained rotation will always be about the center of mass, regardless of where the forces are applied. Also, somewhat counterintuitively, force and torque are independent of each other, that is, an applied force is not 'divided up' into resulting linear and angular effects.

The torque arising from an applied force can be calculated with a fairly simple equation involving the perp-dot product. You can find the equation in the above papers.

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If you define several connected points evenly around the outside of your object and give each of them inertia, rotation and translation should pretty much handle themselves.

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