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Physics LibreTexts

3.9: Comparison

At this stage I compare some somewhat similar formulas.

\(\textbf{L} = \textbf{L}_{C} + \overline{\textbf{r}} \times \textbf{P}\) \(\boldsymbol\tau = \boldsymbol\tau_{C} + \overline{\textbf{r}} \times \textbf{F}\)
\(\textbf{L} = \sum m_{i}\textbf{r}_{i} \times \textbf{v}_{i} \) \(\boldsymbol\tau = \sum m_{i}\textbf{r}_{i} \times \dot{\textbf{v}}_{i}\)
\(\textbf{L}_{C} = \sum m_{i} \textbf{r}_{i}^{'}\times\textbf{v}_{i}^{'} \qquad \) \(\boldsymbol\tau^{'} = \sum m_{i}\textbf{r}_{i}^{'}\times \dot{\textbf{v}}_{i}\)
\(\textbf{P} = \sum m_{i}\textbf{v}_{i} \qquad \)

\(\textbf{F} = \sum m_{i} \dot{\textbf{v}}_{i}\)

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