Loading [MathJax]/extensions/TeX/boldsymbol.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Physics LibreTexts

3.8: Torque

( \newcommand{\kernel}{\mathrm{null}\,}\)

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.

Support Center

How can we help?