Center of Mass : Fundamental Principle in Physics

The center of mass (also called the center of gravity in a uniform gravitational field) is a point in a body or system of particles where all of the mass can be considered to be concentrated for the purposes of analyzing motion :

Here’s a simple overview :

• For a uniform, symmetric object (like a ball or a box), the center of mass is at the geometric center.
• For irregular objects (like a hammer or a person in a specific pose), the center of mass is the point where you could balance the object if it were placed on a pivot.
• In multiple object systems (like the Earth-Moon system), the center of mass is the weighted average of the masses’ positions.

Mathematically, for a system of particles, the center of mass is calculated using:

Where:

• m_i​ is the mass of the individual particle
• r_i is the position vector of the individual particle