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Novice programmer and explorer of simple 2D physics, here.

I have a simple 2D object made up of two rigid bodies connected at a fixed joint.

The two rigid objects can rotate freely about that fixed joint, causing the center of mass and moment of inertia of the whole object to change(but not adding extra energy to the system).

If my 2d object is rotating about it's center of mass, and then the center of mass changes (because one of its components rotates), what happens with the torque?

Since my torque was applied at the initial center of mass, and now the center of mass has changed, it would seem that I could not just preserve the torque for the new object orientation?

One possibility in my head is that some of that initial torque will be converted to linear velocity, but I can't visualize this in any consistent way.

So does the torque value remain the same when center of mass changes or does it need to be recalculated?

What key information am I missing here?

If there's a simple enough answer that could be expressed in some python or pseudo code (in terms of what to do with the torque), that would be appreciated.

EDIT:

I'll try to be more clear. There's no friction there's no gravity, and no ability for either of these objects to collide with anything (they are in vacuum too). The two components themselves are connected at a joint but they are effectively rigid (in the sense that torque force does not cause them to change their orientation to joint). Linear velocity starts at nothing and we apply a one time (impulse?) torque through the center of mass. The whole object rotates in the expected way when all of the sudden one of the components of the object changes its orientation(without adding any additional forces to whole object). This changes the objects center of mass and moment of inertia. Since the only force applied to this object was torque, what happens in such a hypothetical situation? I'm mostly interested in how to apply the existing energy to the new orientation. Does the object gain linear velocity and lose torque? If so how do i calculate that.

(I suppose if I were spinning in outer space and stuck out my arm, that might be along the same line?)

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It seems to me that you haven't defined enough of what is happening in your system, to know how it should move.

I.e., I think you are missing the forces involved when one of the two component objects rotates itself. In real inertial physics, nothing moves without force being applied, but it sounds like your model for the component rotation may not include those forces. It also matters whether the joint is stiff or loose. It may help to think of each component as an object, as well as declaring what force is applied where when one of them tries to rotate itself relative to their connecting point. Are they pushing themselves with thrust from some place on themselves to rotate, or are they applying force to the joint? The point where the force is applied, and the direction of force, determines the effective torque arm. The friction at the joint determines what happens between the two objects as force is applied, and whether each object has inertia relative to the other or not.

Also, is there friction with the environment as these objects rotate, or are they floating in a vacuum?

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If you are trying to deduce difference in force and how it effects a single object with a change to its center of gravity, making each component of that object, a single object and then using its force to calculate any strain or pressure would seem to be the way to do it.

If you have two weights on a bar, and they rotate around the center, and then you want to change that center point of rotation, it would seem that calculating different centrifugal forces for the two different masses moving(the weights) in now different circles(different center of gravity), would give you the pressure on there connecting point the bar.

The torque at a center of a car, is equal to the opposite forces applied from the front and back of the car.

the spinning and sticking out your arm is the ice skater question, you would slow down since some of the mass is traveling a greater distance, or something like that. But to calculate it, make your arm a separate object that then applies the force through the rigid connection. The force your arm would be applying would be its inertial force.

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