# Center of mass

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

Andrew Mason
Homework Helper
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

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.

Dale
Mentor
2021 Award
The center of mass is a position. Technically position is an affine space, not a vector space. At least in non relativistic physics.

Andrew Mason
Homework Helper
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:

$$\vec{R} =\frac{1}{\sum_{i}m_i} \sum_{i} m_i\vec{r}_i$$

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

AM

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