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A force F is continually acting on the end of a solid rod at a pivot point A (see image below). The object causing that continual 'Force F' is attached to pivot point A and constrained to only move in the line of direction shown.

What forces are causing the center of mass (COM) to move in line with the tail end of the force vector F?

I understand that one can assume a ‘moment of a couple’ will be created about the COM, but couples do not physically move the COM. If that is the case, then is it force F causing the COM to move up and to the left?

But how can that be possible because there is no vertical force component for F?

enter image description here

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2 Answers 2

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Consider Newton's Second Law - $$∑F = m a$$

What exactly does a mean here.It refers to acceleration of Centre of Mass of the system.In your question,when you use Newton's Second Law the acceleration term is of Centre of Mass and not that of A.

Get it?

Centre of Mass does not move up. Point A moves down.Centre of Mass moves in a straight horizontal line.

Why does point A moves down?

This is because F provides necessary torque to do so.

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  • $\begingroup$ Hi Tony - I understand what you mean but in my example I meant making force F move in a straight line (as shown in the diagram ) and not allowing point A to move down. If that scenario , what forces will move the COM up? $\endgroup$
    – Dubious
    Aug 20, 2020 at 12:46
  • $\begingroup$ Tony - look at this video below up to 6:01 and you will understand the scenario I'm talking about . vimeo.com/158419250 $\endgroup$
    – Dubious
    Aug 20, 2020 at 13:04
  • $\begingroup$ To prevent A from moving down, an external vertical force must be applied. $\endgroup$
    – R.W. Bird
    Aug 20, 2020 at 15:16
  • $\begingroup$ @Dubious If you take A as your axis of rotation,then COM will rotate due to pseudo torque. This is perhaps what best fits your video. $\endgroup$
    – Tony Stark
    Aug 21, 2020 at 3:02
  • $\begingroup$ @Dubious I have a suggestion. Try asking another question about how dynamics of golf work. $\endgroup$
    – Tony Stark
    Aug 21, 2020 at 11:05
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After much thought I think I have the answer but I had to go through various steps . Please see the diagrams below. For the COM to move up and align itself with force F it seems another force needs to be applied at point A to prevent it spinning around its centre of mass.

STEPS 1-3

enter image description here

enter image description here

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