How to find the centre of mass of a system of three particles?

The centre of mass of a system of three particles is the point where the entire mass of the system can be considered to be concentrated.

Formula (in coordinate form):

For three particles with masses m₁, m₂, m₃ at positions
(x₁, y₁), (x₂, y₂), (x₃, y₃):

Xcm = (m₁x₁ + m₂x₂ + m₃x₃) / (m₁ + m₂ + m₃)
Ycm = (m₁y₁ + m₂y₂ + m₃y₃) / (m₁ + m₂ + m₃)

Steps to Calculate:

1. Multiply each mass with its respective coordinates
2. Add all these values
3. Divide by the total mass

Special Case:

• If all masses are equal, the centre of mass is simply the average of their positions

Example Insight:

If masses are equal:
Xcm = (x₁ + x₂ + x₃)/3,
Ycm = (y₁ + y₂ + y₃)/3

Conclusion:

The centre of mass is calculated as the weighted average of positions of all particles, based on their masses.