Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

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

These terms seem to be used interchangeably.

Is there a difference between them for non-moving object on Earth, or moving objects for that matter?

share|improve this question
    
The Wiki link is very much satisfactory..! –  Waffle's Crazy Peanut Jan 13 '13 at 13:10
    
Of course these are not to be confused with "center of momentum," the rest frame of which is sometimes confusingly called the "center of mass frame." –  Chris White Jan 13 '13 at 14:31
    
In a constant gravitational field (a flat, infinitely large earth would do), they would be the same... But in the case of the earth, the cog would actually be a bit lower than the com. –  Dimensio1n0 Jul 4 '13 at 4:20

4 Answers 4

up vote 5 down vote accepted

The difference is that the centre of mass is the weighted average of location with respect to mass, whereas the centre of gravity is the weighted average of location with respect to mass times local $g$. If $g$ cannot be assumed constant over the whole of the body (perhaps because the body is very tall), they might (and generally will) have different values.

I don't see an immediate connection with movement though.

share|improve this answer

Centre of mass & gravity coincides until they have unifrom gravitational field. The time uniform gravitational field is lost we rather consider centre of mass than centre of gravity. However, they both're interchangeable.

share|improve this answer

Quoting from tha wiki page:

Center of gravity is the point in a body around which the resultant torque due to gravity forces vanish.

That means that for any rigid body, the two points are the same, because you can model rigid bodies in free fall as if gravity acted only on the center of mass, and forces on the center of mass make no torque.

share|improve this answer
1  
This is wrong. They are only the same if the gravitational field is not varying over the extent of the body. –  Jerry Schirmer Jan 13 '13 at 16:39

Center of mass is actually the integral of mass density. Meanwhile, center of gravity is the integral of force of gravity!

share|improve this answer
2  
In both cases you have described the zeroth moment of something when you should mean the first moment. However, the distinction you in terms of what quantity you want to take the moment of is correct. –  dmckee Apr 25 '13 at 0:07

protected by Qmechanic May 3 '13 at 14:09

Thank you for your interest in this question. Because it has attracted low-quality answers, posting an answer now requires 10 reputation on this site.

Would you like to answer one of these unanswered questions instead?

Not the answer you're looking for? Browse other questions tagged or ask your own question.