Why do we need a separate center of gravity idea when we have CoM?

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Discussion Overview

The discussion revolves around the concepts of center of mass (CoM) and center of gravity (CoG), particularly in the context of their relevance in non-uniform gravitational fields. Participants explore the implications of these concepts in relation to motion, rotation, and external forces, examining the necessity of distinguishing between the two ideas.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that the center of mass behaves like a point particle under external forces, even in non-uniform gravitational fields, questioning the need for a separate center of gravity.
  • Others argue that the center of gravity is important for understanding the rotation of a body, as it provides different information compared to the center of mass.
  • A participant notes that the center of mass moves with constant velocity in a closed system, while external forces complicate its motion in non-homogeneous fields.
  • Some contributions suggest that the center of gravity serves as a representative point for the application of gravitational forces, differing from the center of mass which represents the distribution of mass.
  • There is a discussion about whether the concept of a center of external forces could be defined in scenarios with multiple forces acting on a rigid body.
  • Participants highlight that the center of gravity can create torque around the center of mass if they are not coincident.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and implications of the center of gravity versus the center of mass, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

The discussion includes assumptions about the nature of gravitational fields and external forces, with some participants emphasizing the limitations of applying the center of mass concept in non-uniform fields.

  • #31
kuruman said:
Isn't that what I have?
Sorry I was viewing it on mobile. I had to slide it to see it full
 
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  • #32
Ryder Rude said:
The center of mass point literally follows the path that a particle of mass M would've followed if the forces on the system were thought of as directly acting on that point.
If the center of gravity (or buoyancy or any other distributed force) is different from the center of mass then the force acts through the center of gravity (etc) and therefore produces a torque about the center of mass. The motion of the body then cannot be described simply by the path of the center of mass. The object will rotate about the center of mass. Modeling this torque is the reason for distinguishing the center of mass from the center of gravity (etc).
 
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