I'm working on a sandbox game that allows the player to build a spacecraft and attach thrusters in arbitrary locations on the hull of the spacecraft. The game is set completely in 2D. (I'm a programmer, not a physicist, so I apologize if my terminology is all wrong).
I have need to actually calculate my own physics. Say the player makes a simple spacecraft as follows:
where "A" are the thrusters pointing down, "O" is the cockpit and just so happens to be the center of mass as well, and "=======" is just some metal bar joining everything together. We can completely ignore the existence of any gravity.
Both thrusters are identical and, when turned on, produce an upward force of F at the point of the thrusters. The torque about the CoM for the left one completely cancels out the torque of the right one - hence the net torque is zero. The resultant force at the CoM (I believe) is 2*F up. Therefore, the ship accelerates up - there is no sideways acceleration and no torque to cause the craft to rotate.
What if only the right-side thruster is fired while the left one is left off? There would be a net anti-clockwise torque on the craft but I believe there is also some resultant force on the CoM as well? Torque I know how to calculate, but what about this resultant force vector?
I'm trying to relate this to the experience of flicking the tip of a pen resting on a table top. There would be torque because I observe the pen spinning, but there would also be some resultant force because the pen is also sliding down the table.