Center of Mass Acceleration

Summary

Center of mass in terms of acceleration describes the acceleration of the center of mass point.

Key Equations:

Center of mass acceleration:
$a_{c m} = \frac{\sum_{i} m_{i} a_{i}}{\sum_{i} m_{i}}$

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Definition

Center of mass in terms of acceleration describes the acceleration of a point as if all the mass were centred on a point. By definition of acceleration it's the derivative of the center of mass velocity.

\begin{aligned} a_{c m} & = \frac{d r}{d t} v_{c m} \\ = \frac{\sum_{i} m_{i} a_{i}}{\sum_{i} m_{i}} \end{aligned}