What is the relationship between center of mass and center of gravity?

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Discussion Overview

The discussion explores the relationship between the center of mass and the center of gravity, focusing on their definitions, dependencies, and differences in various gravitational fields. It includes conceptual clarifications and technical reasoning regarding gravitational effects on objects.

Discussion Character

  • Conceptual clarification, Technical explanation, Debate/contested

Main Points Raised

  • One participant asks for examples of objects where the center of mass and center of gravity differ.
  • Another participant states that the center of gravity is not an intrinsic property and depends on the gravitational field, noting that it is typically below the center of mass in the field of a spherical object like Earth.
  • A follow-up question seeks clarification on why the center of gravity is below the center of mass and why this difference decreases with distance from the gravitating body.
  • A participant explains that the non-uniformity of the gravitational field causes the lower half of an object to experience a stronger pull, leading to the center of gravity being lower, and that this effect diminishes with distance due to the inverse square law of gravity.
  • It is noted that for ordinary-sized objects near Earth's surface, gravity can be treated as uniform, which leads to the common practice of equating center of gravity with center of mass in introductory texts.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between center of mass and center of gravity, particularly regarding the conditions under which they differ. The discussion remains unresolved with multiple perspectives presented.

Contextual Notes

Limitations include the assumption of uniform gravitational fields for ordinary-sized objects and the dependence on the specific gravitational field being considered, which may not be universally applicable.

texasratt
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Can anyone give me an object where the center of mass and the center of gravity are in different locations?
 
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The center of gravity is not an intrinsic property of an object. It depends on the gravitational field the object is in. In the gravitational field of a spherical object (like, say, the Earth), and object's center of gravity will always be slightly below its center of mass; but, the farther it is from the center of the gravitating body, the smaller this difference.
 
why is it below and why does this get smaller with distance?
 
texasratt said:
why is it below and why does this get smaller with distance?
Because the gravitational field is not uniform: It's stronger the closer you are to the spherical object, so the lower half is pulled more strongly than the upper half. Since the field falls off inversely with the square of the distance, the farther away you are the less it matters.

Note that for ordinary-sized objects near the Earth's surface, Earth's gravity can be considered uniform for practical purposes. That's why many introductory texts treat "center of gravity" as synonymous with "center of mass".
 

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