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3.8: Torque

  • Page ID
    8380
  • [ "article:topic", "torque", "authorname:tatumj", "showtoc:no" ]

    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

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

    Thus: 

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

    therefore

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

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