Classical Mechanics p65 PDF
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The document details equations and concepts related to the center of mass of a physical system. It includes equations for total momentum, velocity, and force, as well as the behavior of the center of mass when external forces are present or absent. It also includes relevant diagrams to aid in the understanding.
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## 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.
