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

AI Thread Summary
The center of mass is a point that can be expressed as a displacement vector from the origin of a reference frame. It is not a vector quantity in the traditional sense, as it represents a position rather than a vector space. In non-relativistic physics, the center of mass of a mass distribution is calculated using the sum of point masses multiplied by their displacement vectors divided by the total mass. This concept is crucial for understanding motion and forces in classical mechanics. The discussion clarifies that while the center of mass can be represented as a vector, it fundamentally describes a position in space.
oreo
Messages
81
Reaction score
2
Is center of mass a vector quantity. If so then how? Is it directed towards Earth's center?
 
Physics news on Phys.org
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
 
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.
 
The center of mass is a position. Technically position is an affine space, not a vector space. At least in non relativistic physics.
 
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:

Thread 'Need help understanding particle physics and quantum physics'

So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
View full post »

Similar threads

I Center of Mass of a jetpack-Earth System
Replies
7
Views
3K
B Is Center of Mass a vector or scalar quantity?
Replies
31
Views
9K
B Can Earth or any spherical object in space act as a particle collider?
Replies
6
Views
2K
I Stable solutions to simplified 2- and 3-body problems?
Replies
6
Views
3K
I Understanding Ewald's sphere in the context of X-Ray diffraction
Replies
3
Views
5K
I Center of Mass of Quarter-Circle Wire
Replies
3
Views
14K
B Gravitation with multiple objects by using center of mass
Replies
7
Views
2K
I Is the position vector a real vector?
Replies
8
Views
3K
I Rigid body physics (machine learning environment)
Replies
2
Views
1K
B How to track the center of mass of a human in a video
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top