Can Multiple Forces on a Body Be Simplified for Motion Analysis?

[yahastu]

Consider a free-falling object with known mass and center of mass being acted upon by four forces -- force of gravity at the center of mass, as well as three additional force vectors applied at known positions on the body. Is it possible to calculate, in closed form, the position and orientation of the object after a specific elapsed time t?

Is it valid to simply compute the net force vector and apply it to the COM, and then treat the COM as a fixed axis, and convert all the forces into torques and compute the net angular rotation?

 

[kuruman]

Hi yahatsu and welcome to PF.

Is it valid to simply compute the net force vector and apply it to the COM, and then treat the COM as a fixed axis, and convert all the forces into torques and compute the net angular rotation?

Yes, it is valid and often appropriate to separate the motion of the center of mass from the motion about the center of mass.