It's not a homework problem as I am way too old already but it's something that had made me given problem getting to sleep. I'm probably missing smthg. let's say you have a horizontal uniform rod lying on ice such as there is no friction and the normal force equal the weight of the rod. Let's say the left end of the rod is at x=0 and the right end is at x=L now 10N force is applied in the +Y direction at X=L and a force of 10N is applied in the -Y direction at X=0,9L. No other forces acts on the rod therefore : the acceleration of the center of mass should be 0 and if we assume the rod is not moving before the forces are applied then the center of mass at X=L/2 should be fixed. This is somewhat hard for me to vizualize , try this with a pen lying on a table and apply two approx equal force in the opposite direction at two points near one end of the pen you can clearly see a shift of the pen toward one direction the COM is clearly moving. Moreover in the example above if you calculate the rotation about x=0 due to the torques you have something like Torque=10N*1L-10N*0,9L... whatever result there is an angular acceleration about x=O making the rod rotate about it . I understand that the point on the rod at x=O is not fixed , is that the origin of my problem ? there is actually a rotation around x=0 but there is also a translational motion of x=0 such that the rotation about it + the T motion make the actual COM fixed when you sum the effects ??? and so the example with the pen on the table is not a good example for visualizing the problem ??