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I am not sure if I am asking a very complicated question but I want to know exactly what is happening at the molecular level that exerting force along center of mass produces linear motion and not torque and force away from COM produces torque and not pure linear motion. Does force not get distributed properly or something when force is away from COM thus producing torque where individual molecules of an object move at different velocity, acceleration. If this is part of the explanation, what is the mechanism for this. I have searched the net exhaustively for an intuitive and non mathematical explanation and so far I feel like I have not progressed as all on this question. Can anyone please give a non-mathematical explanation for why this is so?

Qmechanic
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TLo
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    Does this answer your question? Why does a body not rotate if force is applied on the centre of mass? – Sandejo Nov 15 '20 at 18:22
  • Hi Sandejo. I am not sure of what to make of the link you posted. i think problem is that I don't have a background in calculus so lot of the mathematical explanation just escapes my understanding. I was looking for a more theoretical, layman's explanation but I wonder if this question is such that it becomes hard to explain without involving numbers and equation. – TLo Nov 15 '20 at 18:44
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    There is no reason to ask for an explanation at "molecular level". It's just from the definition of torque. If the direction of the force goes through a given point, the torque is zero relative to that point. The torques is not zero relative to other points so the object may rotate about arbitrary points, even if the force goes throuh the COM. – nasu Nov 16 '20 at 13:22
  • Hi Nasu. I just saw your response. I wanted to know what do you mean by it just being the definition of torque? I wanted to know the why behind that definition. I mean a definition has to be a reflection of some mechanism or process based on reality right? Or is it just a arbitrary convention invented or set by humans to make things easier to understand? – TLo Dec 02 '20 at 02:29

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The COM can be considered the balance point of the entire object. Applying a force to the COM will move the entire object evenly as there will be a balance of the mass on any side of the line of force with the exact opposite side so it translates but does not rotate or tilt, as it is in balance. Now if you apply the force off center, not in line with the COM, one side of the line of force will not be in balance with its opposite side. So it will rotate and translate.

Adrian Howard
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  • For one thing, a point does not have "one side" or the "opposite side". If you reffer to the line along whch the force acts, even when it goes through the COM it is not necesarily true that there is the same mass on both sides. – nasu Nov 16 '20 at 13:20
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Torque is defined relative to some chosen (often fixed) axis of rotation. Is is best defined as the work per unit angle of rotation (in J/radian) that can be done by a force acting in a manner that would tend to cause a rotation. The work is done by the component of force which can move along an arc. That component must be perpendicular to the radius measured from the axis to the point of application of the force. In your problem, the axis is assumed to go through the center of mass, and you are concerned about a force which points at the center of mass. It has no component perpendicular to the radius, does not tend to produce a rotation, and produces no torque relative to the center of mass.

R.W. Bird
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