Understanding the Phenomenon in the Attached Picture

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firavia
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please explain to me this phenomena (Details in the picture attached)

- after answering my 2 questions , I would like to make a modification in the picture , the modification is : shifting the force F 1 to the left for 0.5 m , after shifting it 0.5 m would we have a moment at "B" and at "A" , please explain why if yes and and if there was a moment on "A" and "B" in the first condition explain it why , though as I know , free end bodies cannot have moments explain , Am I CONFUSING BETWEEN STATICS AND DYNAMIC EXPLAIN THE DFFERENCE , thnx
 

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If I understand your diagram, the object pictured is accelerating. Taking moments about some point is only useful if that point is the center of mass or is not accelerating. In this case, points A and B are neither.