Centre of Mass for a Two-Particle System

Centre of Mass (CM)

The unique point where the weighted relative position of the distributed mass sums to zero. For a system of particles, it's the average position of all parts of the system, weighted according to their masses.

Position Vector

A vector that describes the position of a point in space relative to an origin.

Position Vector of Centre of Mass (Two Particles)

where m1, m2 are masses and r1, r2 are their position vectors.

R_CM = \frac{m₁ \vec{r}_1 + m₂ \vec{r}_2}{m₁ + m₂}

X-coordinate of Centre of Mass (Two Particles)

for particles along the x-axis.

X_CM = \frac{m₁ x₁ + m₂ x₂}{m₁ + m₂}

Y-coordinate of Centre of Mass (Two Particles)

for particles in the xy-plane.

Y_CM = \frac{m₁ y₁ + m₂ y₂}{m₁ + m₂}