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3.8: Torque

  • Page ID
    8380
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    Notation:

    • \( \boldsymbol\tau_{C} \) = vector sum of all the torques about C.
    • \( \boldsymbol\tau\) = vector sum of all the torques about the origin O.
    • \(\textbf{F}\) = vector sum of all the external forces.
    Theorem

    \[ \boldsymbol\tau = \boldsymbol\tau_{C} + \overline{\textbf{r}} \times \textbf{F} \nonumber \]

    Thus:

    \[\begin{align} \boldsymbol\tau &= \sum \textbf{r}_{i} \times \textbf{F}_{i} = \sum (\textbf{r}'_{i} + \overline{\textbf{r}}) \times \textbf{F}_{i} \\ &= \sum \textbf{r}'_{i} \times \textbf{F}_{i} + \overline{\textbf{r}} \sum \textbf{F}_{i} \end{align} \nonumber \]

    therefore

    \[\qquad \boldsymbol\tau = \boldsymbol\tau_{C} +\overline{\textbf{r}} \times \textbf{F} \nonumber \]


    This page titled 3.8: Torque is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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