Centre of Mass

Centre of Mass

Centre of mass is the point where the entire mass of a system can be considered to be concentrated for translational motion.

### Formula

$$\vec{R}_{cm}=\frac{m_1\vec{r}_1+m_2\vec{r}_2+...+m_n\vec{r}_n}{m_1+m_2+...+m_n}$$

### Two Particle System

$$\vec{R}_{cm}=\frac{m_1\vec{r}_1+m_2\vec{r}_2}{m_1+m_2}$$

### Terminologies

- Rcm → Position vector of centre of mass.

- m₁, m₂ → Masses of particles.

- r₁, r₂ → Position vectors of particles.

### Conditions / Special Cases

For equal masses:

$$R_{cm}=\frac{r_1+r_2}{2}$$

For a symmetric body:

$$R_{cm}=Geometric\ centre$$

### Usage

- Used in motion of systems of particles.