Is the center of mass truly where all forces act in a system?

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SUMMARY

The center of mass in a system of particles or a rigid body is a theoretical point where the vector sum of all external forces is considered to act during translatory motion. While it simplifies calculations, forces do not physically apply at this point, as demonstrated by torque acting on a rigid body, where forces must act at specific points to induce rotation. In scenarios where particles maintain their relative positions, it is valid to treat the center of mass as the point of force application, exemplified by a coat hanger whose center of mass is often in mid-air.

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  • Understanding of Newtonian mechanics
  • Familiarity with the concept of torque
  • Knowledge of rigid body dynamics
  • Basic principles of translatory motion
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physics user1
As far as I know in a system of particles or a body there is a point that behaves like all the forces on the system are applied at this point, but are these forces really applied in this point? Can you explain please, I thought at this and I arrived at the conclusion that these forces aren't really applied there since in the center of mass of a system there isn't necessarily a particle and a force applied to "nothing" have not sense
 
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For the purpose of mathematical simplicity, it is assumed that, when the body is undergoing translatory motion only, the vector sum of all external forces act on it's center of mass.
However, as you rightly pointed out, it is implausible to take this a general principle.
Take the simplest case of torque acting on a rigid body: Here, the force acts at a given point which makes the body rotate about an axis (it is important that the force act elsewhere and not on the center of mass if the body is under no other force).
In the sense of system of particles, if the particles of the system don't change their position relative to each other it is safe to conclude that all the external force acting on the system is at the center of mass of the system.
 
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A coat hanger is a classic example of a rigid object whose center of mass is usually in mid air.
 

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