Center of mass vs. center of gravity

In summary: I'm not really sure what you're asking here. Can you clarify?Yes, the centre of gravity is the point that the gravitational force is the same in all directions. It is also the point where the gravitational force is directed towards.
  • #1
pierce15
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Are there any realistic scenarios for which center of mass is not almost exactly equivalent to the c.o.g., i.e. they must be treated separately?
 
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  • #3
from looking at that wiki link, I'd guess a useful application is for spherical gravitational field (like that from the Earth). So, say we were talking about the torque on a satellite (or spaceship) due to Earth's gravity, then we could use the term center of gravity in a useful way. (i.e. the center of gravity of the spaceship would be different to its center of mass).

Although, the gravitational force is going to be pretty much uniform over a normal-sized spaceship. So I guess the center of gravity would only be significantly different from the center of mass if we had a really huge spaceship. That would be cool. Would get in the way of the sun though... people might not be happy about that.
 
  • #4
I think the main part is that the cog is defined and calculated wrt a particular gravitational field while the com just depends on the object.

thus: there would be no center of gravity wrt an external field if the field were zero at the object, but each part of the object would have a cog wrt the combined gravity of all the other bits.

I imagine there may be differences in a non-inertial frame too. but I'm too lazy right now to check properly.
The "related discussions" list below is neat reading though.
 
  • #5
cool, so maybe it is useful concept for a spiral galaxy, to talk about the centre of gravity of one of the arms with respect to the gravity caused by the rest of the galaxy.
 
  • #6
A good demonstration of the dramatic possible difference between centre of mass and the centre of gravity would be to consider the cm of the Earth and Moon (that's somewhere below the surface of the Earth, as it happens)
The, if you take the Centre of Gravity as the point which attracts another nearby object, ask yourself, if you stood on the Moon, would you be attracted to the CM of the Earth Moon system? The Centre of Gravity, for someone on the Moon will be beneath their feet and 'in the Moon'.

CM is always the same. CG depends upon your reference point
 
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  • #7
sophiecentaur said:
CM is always the same. CG depends upon your reference point
I don't really understand this. If it is possible to say the CG depends on reference point, then isn't it equally as valid to say the CM depends on reference point? Like for example, if we say "the CG due to only gravity caused by the moon" then we could also say "the CM due to only mass of the moon"
 
  • #8
Centre of Mass is defined as the point in / on the object where the sum of the moments about it is Zero. It is just referenced to the object itself (and the distribution of masses within it). CG is where the force of gravity acts when in another gravitational field.* If the other field is uniform then the CM and CG happen to be in the same place but not generally. (It also applies to two uniform spheres.)


*The word 'Field' means the description of how the force on a 'unit mass' varies over a region of space. You can consider the field of the EarthMoon OR the field of the observer / object. You will get the same answer for the force and its direction whichever you choose to take as the field generator and which you choose to be the 'test object'. (The sign of the force will need to be adjusted, depending which is the attractor and which is the attracted .)
 
  • #9
ah right. I would have assumed that the CG is also due to the gravitational field of itself. But if that is not how CG is defined, then yeah, I can see what you mean now.
 

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 the force of gravity acts upon an object. In a uniform gravitational field, the center of mass and center of gravity will be the same point. However, in non-uniform fields or when considering objects with varying densities, the two points may differ.

2. How is the center of mass calculated?

The center of mass is calculated by taking the weighted average of the positions of all the particles that make up an object. This means that the mass of each particle is multiplied by its distance from a chosen reference point, and the sum of these values is divided by the total mass of the object.

3. How is the center of gravity different on Earth compared to other planets?

The center of gravity is determined by the distribution of mass within an object, as well as the gravitational field in which it is located. On Earth, the center of gravity is closer to the center of the planet due to its relatively uniform density. However, on other planets with different densities or non-uniform gravitational fields, the center of gravity may be located at different points within the object.

4. What is the significance of the center of mass and center of gravity in objects?

The center of mass and center of gravity are important for understanding how objects move and interact with their surroundings. They are also crucial for determining an object's stability and balance. In addition, these points are used in engineering and design to ensure that structures and machines are properly balanced and can safely support their own weight.

5. Can an object have multiple centers of mass or gravity?

No, an object can only have one center of mass and one center of gravity. However, in some cases, an object may have multiple points that can be considered as its center of mass or gravity, depending on the reference point used. For example, a ring-shaped object may have multiple points where its mass is evenly distributed, but the overall center of mass and gravity will still be at the center of the ring.

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