# Center of mass

1. Jan 10, 2015

### oreo

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

2. Jan 10, 2015

### Andrew Mason

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

3. Jan 10, 2015

### oreo

Thanks a lot.

4. Jan 10, 2015

### Staff: Mentor

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

5. Jan 10, 2015

### Andrew Mason

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

Last edited: Jan 10, 2015