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

In summary, the center of gravity is not an intrinsic property of an object and depends on the gravitational field it is in. For a spherical object like the Earth, the center of gravity is always slightly below the center of mass, but the difference decreases with distance due to the non-uniformity of the gravitational field. However, for most everyday objects on the Earth's surface, the difference is negligible and the terms "center of gravity" and "center of mass" can be used interchangeably.
  • #1
texasratt
3
0
Can anyone give me an object where the center of mass and the center of gravity are in different locations?
 
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  • #2
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.
 
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why is it below and why does this get smaller with distance?
 
  • #4
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".
 

1. What is the difference between center of mass and center of gravity?

The center of mass is the point at which an object's mass is evenly distributed, while the center of gravity is the point at which an object's weight is evenly distributed. In most cases, these two points are the same, but in cases where there is a significant difference in gravitational pull, such as near a black hole, the center of gravity may differ from the center of mass.

2. How is the center of mass/gravity calculated?

The center of mass/gravity can be calculated by finding the weighted average of an object's individual parts. This is done by multiplying the mass of each part by its distance from a chosen reference point, and then dividing the sum of these products by the total mass of the object.

3. Why is the center of mass/gravity important?

The center of mass/gravity is important because it helps us understand how an object will behave when subjected to external forces. It also helps engineers design stable structures and vehicles, as well as helps athletes and dancers maintain balance and control.

4. Can the center of mass/gravity be outside of an object?

No, the center of mass/gravity must always be located within the boundaries of an object. However, in some cases, it may appear as though the center of mass/gravity is outside of the object, such as in a leaning tower, but this is due to the distribution of mass within the object.

5. How does the center of mass/gravity change with different shapes?

The center of mass/gravity can change depending on the shape and distribution of mass in an object. For example, a solid sphere has its center of mass at its geometric center, while a hollow sphere's center of mass is closer to its outer surface. Generally, objects with more mass towards the bottom have a lower center of mass/gravity, making them more stable.

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