Centre of mass formula?

The formula for calculating the center of mass of an object is:

\[ \text{Center of mass} = \frac{\sum m_i \cdot r_i}{\sum m_i} \]

Where:
- \( m_i \) is the mass of each individual component of the object
- \( r_i \) is the position vector of each individual component of the object

Centre of Mass Formula for a System of Point Masses

For a system of n point masses, each with mass m and position vector r, the centre of mass R is given by:

```
R = (1/M) - Σ (m - r)
```

where:

- M is the total mass of the system, defined as the sum of all the masses: M = Σ m
- m is the mass of each point mass
- r is the position vector of each point mass, relative to a common origin

Vector Form:

```
R = (1/M) - (Σ m - r)
```

Component Form:

```
Rx = (1/M) - Σ (mx)
Ry = (1/M) - Σ (my)
Rz = (1/M) - Σ (mz)
```

where:

- Rx, Ry, Rz are the components of the centre of mass vector R
- mx, my, mz are the components of the position vectors r