Center of mass

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Main Question or Discussion Point

Is center of mass a vector quantity. If so then how? Is it directed towards Earth's center?
 

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Andrew Mason
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Is center of mass a vector quantity. If so then how? Is it directed towards Earth's center?
The centre of mass is a point. As such, it is expressed as a displacement vector from the origin of the reference frame that is being used. If it coincides with the origin, it is the vector (0, 0, 0).

AM
 
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The centre of mass is a point. As such, it is expressed as a displacement vector from the origin of the reference frame that is being used. If it coincides with the origin, it is the vector (0, 0, 0).

AM
Thanks a lot.
 
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The center of mass is a position. Technically position is an affine space, not a vector space. At least in non relativistic physics.
 
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Andrew Mason
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Shayan,

Just to follow up on this, the centre of mass of a mass distribution is conveniently expressed as the sum of each of the point masses in the system multiplied by their displacement vector from the origin divided by the total mass:

[tex]\vec{R} =\frac{1}{\sum_{i}m_i} \sum_{i} m_i\vec{r}_i[/tex]

See, for example, Barger & Olson, Classical Mechanics, A Modern Perspective, first ed., ch. 5-1, p. 156-160

AM
 
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