Classical Mechanics p65 PDF

## Center of Mass of System Definition **Center of Mass:** - $ \overrightarrow{P}_{tot} = M_{tot} \overrightarrow{V}_{cm}$ - $\frac{d\overrightarrow{P}}{dt} = \overrightarrow{F}_{tot}^{ext} = M_{tot} \overrightarrow{a}_{cm}$ **Behavior of CM** - Is predictable - If $\overrightarrow{F}_{ext} = 0...

## Center of Mass of System Definition **Center of Mass:** - $ \overrightarrow{P}_{tot} = M_{tot} \overrightarrow{V}_{cm}$ - $\frac{d\overrightarrow{P}}{dt} = \overrightarrow{F}_{tot}^{ext} = M_{tot} \overrightarrow{a}_{cm}$ **Behavior of CM** - Is predictable - If $\overrightarrow{F}_{ext} = 0$, it will continue with the same velocity **Notes** - The center of mass itself may be tumbling. - In any object, the center of mass behaves as if all matter were together in one point. **Equations** - $M_{tot} \overrightarrow{V}_{cm} = \sum_i m_i \overrightarrow{V}_i$ - $\overrightarrow{V}_{cm} = \frac{1}{M_{tot}} \sum_i m_i \overrightarrow{V}_i$ - $\overrightarrow{V}_{cm} = \frac{1}{M_{tot}} \overrightarrow{P}_{tot}$ - $\overrightarrow{P}_{tot} = M_{tot} \overrightarrow{V}_{cm}$ - $\overrightarrow{F}_{tot}^{ext} = M_{tot} \overrightarrow{a}_{cm}$ **Description** The image shows a blackboard with various equations related to the center of mass of a system. The blackboard is divided into two sections, the left side shows a diagram of a system of masses and the right side shows equations for the center of mass, momentum, and force.