I've been diving into dynamics these days as part of my Education in mathematics, but I'm having some problems. One, very particularly biting problem, is that of equilibirum.

Wikipedia states Equilibirum as: "A system is in mechanical equilibrium when the sum of the forces, and torque, on each particle of the system is zero".

This is the definition I have been taught with. I was also taught that when in equilibirum, a system/object has a resultant force of zero in ANY direction/axis. Finding resultant forces was easy when they were all passing through the centre of gravity of an object. But now, as I try to solve scenes of rigid bodies, where there are several forces, with part of them NOT applying on the centre of gravity, I get confused.

See, it's because of this simple example:

A ladder of uniform mass and length (2L) is lying on the floor, horizontally. It has weight, which is being neutralised by the reaction force from the ground. But, there are two forces applying, upwards, at the edge of the ladder, both of magnitude 7N. Thus, their moments cancel, as both their moments are (7L), but in the opposite directions. But how the heck do the sum of forces here result in zero??????????? You can change the question by converting the ladder into a ball, or you can resposition or increase the number of moment-producting forces as long as their moments nullify and yet they remain parallel and in one direction. How do the sum of forces in a direction result in zero in such cases, even when the object is at equilibirum???? If the sum of forces in one direction is not true here, then how can it be true for a case where a ladder has one end on the ground, and the other on a wall, when all the reaction and friction forces which produce torque?