# Principle of transmissibility of forces

I have to admit that I do not understand why the principle of transmissibility of forces works. The textbook states:

The conditions of equilibrium or of motion of a rigid body will remain unchanged if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and same direction, but acting at a different point, provided that the two forces have the same line of action

Ok, let's assume that I have some almost two-dimensional (Its hight is small) rectangular object. It has vertices A, B, C and D. In the first case, I attach a string to C and apply a constant force F (at a time t=0) parallel to the edge CD. After some time, t, passes, the line which connects point C with the center of mass of my rectangle will be parallel to the direction of the force F ( at first the rectangle rotates counterclockwise and then just slides in the direction parallel to force F).

In the second case, I attach my string to point D and apply the same constant force F parallel to CD ( so the line of action is the same as in the first case). Again, after some time t, the line which connects point D with the center of mass of my rectangle will be parallel to the direction of the force F and my rectangle will just slide in the direction parallel to the applied force.

However, in the second case, point C will be located to the left of the line which connects the center of mass and the point to which force F is applied (please, see attached image). This means that my rectangular object undergoes, in the second case, rotation on a larger angle. So, in the end, I get different results. I would be grateful if someone explained to me where I am making a mistake.

The forces in each case are not acting through the same line of action after $$t=0$$, so the part you quote no longer applies. Note that the quote does not say that the same line of action at one instant in time is sufficient for the motion / equilibrium to be the same.