Curvilinear motion of force-couple system

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Fishon91
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I have a system of forces which I have reduced to a force-couple system. I am trying to predict the motion of the force and couple. This is hard because the force changes direction as the moment turns the particle. I imagine this should be turned into some sort of tangential-normal components. But which force causes tangential acceleration, and which force causes normal aceleration. The force or the moment?
 
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In the attached photo A, L, D and Phi are constants. There is a torque and a force applied to this box, or whatever it is. In front of the box is what I imagine the motion caused by the force and the torque will make the box go in.
 

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I think the question is probably one where the box has both rotational acceleration and translational acceleration. I am not sure you have analysed the problem correctly. A torque should be two balanced forces with a spacing between their lines of action. You seem to be giving the box an upward acceleration but I cannot see a force doing that.
 
The picture is a top view, not a side view. The picture is displayed in the X-Y plane.