Understanding Center of Mass: Is it a Vector Quantity & Its Direction?

In summary, the center of mass is a point that is expressed as a displacement vector from the origin of the reference frame. It is not a vector quantity, but can be expressed as a sum of point masses multiplied by their displacement vectors. It is not necessarily directed towards Earth's center, but can coincide with the origin of the reference frame.
  • #1
oreo
81
2
Is center of mass a vector quantity. If so then how? Is it directed towards Earth's center?
 
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  • #2
shayan haider said:
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
 
  • #3
Andrew Mason said:
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.
 
  • #4
The center of mass is a position. Technically position is an affine space, not a vector space. At least in non relativistic physics.
 
  • #5
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
 
Last edited:

1. What is the definition of center of mass?

The center of mass is the point at which the entire mass of a body can be considered to be concentrated for the purpose of calculating its motion.

2. Is center of mass a vector quantity?

Yes, center of mass is a vector quantity because it has both magnitude and direction. It can be represented by an arrow pointing towards the direction of the combined mass.

3. How is center of mass calculated?

Center of mass can be calculated by taking the weighted average of the positions of all the particles in a system. This means that the position of each particle is multiplied by its mass, and then all the results are added together and divided by the total mass of the system.

4. Can the center of mass be outside of an object?

Yes, the center of mass can be outside of an object. This can happen if the distribution of mass within the object is not symmetrical or if there are external forces acting on the object.

5. How does the direction of the center of mass affect an object's motion?

The direction of the center of mass affects an object's motion because it determines the direction in which the object will move if acted upon by an external force. The object will accelerate in the direction of the net external force, which is determined by the direction of the center of mass.

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