Saved Bookmarks
| 1. |
Show that moment of a couple does not depend on the point about which you take the moments. |
Answer» SOLUTION : Consider a couple as shown in Fig. 7.22 ACTING on a rigid body. The forces `F and -F` act respectively at points B and A. These points have position vectors `r_(1) and r_(2)` with respect to origin O. Let us TAKE the moments of the forces about the origin. The moment of the couple = sum of the moments of the two forces making the couple `=r_(1)xx(-F)+r_(2)xxF` `=r_(2)xxF-r_(1)xxF` `=(r_(2)-r_(1))xxF` But `r_(1)+AB=r_(2)`, and hence `AB=r_(2)-r_(1)`. The moment of the couple, therefore, is `AB × F`. Clearly this is INDEPENDENT of the origin, the point about which we TOOK the moments of the forces. |
|