Center of Mass

Center of Mass is a point which behaves as though the entire mass of the body/system of particles is concentrated at that point.

For systems of particles:

$$x_{\text{COM}}=\frac{m_1{x}_1+...m_n{x}_n}{m_1+...+m_n}$$

For solid bodies:

$$x_{\text{COM}}=\frac{1}{M}\int x\cdot dm$$