> [!summary] The center of mass is a point where all the mass can be imagined to be located. > **Key Equations:** > COM for Descrite Masses: $\vec{R}_{cm} = \frac{1}{M} \sum_{i} m_{i}r_{i}$ > COM for Continuous Masses $\vec{R}_{cm} = \frac{1}{M} \int r dm$ >[!info]+ Read Time **⏱ 1 min** # Definition The center of mass (COM) is a point where the average location of all the mass is. A point where you can imagine "all" the mass being located at. The location of the COM is a [[Scalar & Vectors|vector]] relative to a reference point, which can be arbitrarily chosen. Mathematically, it is defined below, where $m_{i}$ and $r$ is the [[Displacement|displacement]] from the reference point and $M$ is the total mass. $ \begin{array}{c} \text{Descrite Masses}\\ \vec{R}_{cm} = \frac{1}{M} \sum_{i} m_{i}r_{i} \\ \\ \text{Continous masses} \\ \vec{R}_{cm} = \frac{1}{M} \int r dm \end{array} $ > [!bug] Common Misconception [[Moment of Inertia|Moment of Inertia]] describes how mass is disturbed relative to an axis. Center of Mass describes a point where you can imagine all the mass to be located at relative to a reference point. # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/a4KhrJJvD3w?si=-lsb8bRTP2xknhDU" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>