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

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The discussion centers on the distinction between the center of mass (CoM) and the center of gravity (CoG) in the context of external forces, particularly in non-uniform gravitational fields. The CoM represents the point where the mass of a system can be considered to act, while the CoG serves as a point of application for gravitational forces, which can differ from the CoM when rotation and torque are involved. The need for a separate CoG arises because the behavior of a system under non-uniform gravitational forces complicates the motion of the CoM, making it less convenient for calculations. The conversation also touches on the concept of a "center of external forces," which could theoretically summarize the effects of multiple forces acting on a rigid body, but is not commonly used in practice. Ultimately, both CoM and CoG are essential for understanding dynamics in different contexts, particularly when considering rotational effects.
  • #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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