> [!summary] Center of mass in terms of acceleration describes the acceleration of the center of mass point. > **Key Equations:** > Center of mass acceleration: $a_{cm}=\frac{\sum_{i}m_{i}a_{i}}{\sum_{i}m_{i}}$ >[!info]+ Read Time **⏱ 1 min** # Definition Center of mass in terms of acceleration describes the [[Acceleration|acceleration]] of a point as if all the mass were centred on a point. By definition of [[Acceleration|acceleration]] it's the [[Derivative|derivative]] of the [[Center of Mass Velocity & Momentum|center of mass velocity]]. $ \begin{align*} a_{cm} &= \frac{dr}{dt} v_{cm} \\ &= \frac{\sum_{i}m_{i}a_{i}}{\sum_{i}m_{i}} \end{align*} $