Adding multiple torque vectors together to determine resultant torque

I am working in a 2D environment, where there are multiple angular forces (torque) applied at an object. The way I calculated 1 torque "application", was by:

momentarm(MA) = PointApplication - CenterOfMass
ParallelComponent(PC) = MA * (F · MA / MA · MA)
AngularForce(AF) = Force(F) - PC
Torque = AF * ||MA||

And finally

AngularAcceleration = Torque / RotInertia

I anticipate that I will have to change up the angular acceleration formula, if I want to calculate the angular acceleration from multiple torque vectors.

What approach do I have to take to achieve this?

Note that there are no constraints or restrictions around the axis of rotation, and the forces usually aren't symmetrical, but it can happen sometimes.

• Is the axis of rotation fixed by a constraint? May 11 '16 at 8:56
• @CuriousOne No, there are no restrictions or constraints. May 11 '16 at 8:57
• But in 2d, right, so you can avoid the difficulties of the 3d case (which are non-trivial)? In that case you only have to deal with possible translations and the scalar sum of all torques. May 11 '16 at 9:02
• @CuriousOne And how would I find and use that scalar some in the angular acceleration formula? If you could put that in an answer please. May 11 '16 at 9:03
• If you are dealing with real torques (i.e. all forces come in pairs that attach to the rotating body symmetrically, so there is no translation in addition to the change in rotation), then you can simply add the torques all up. If the forces that are attaching to the body are not symmetric, then there is also a component that causes an acceleration of the center of mass. I don't know which of the two cases you are looking at? May 11 '16 at 9:06