13. Moments
From Mechanics
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| - | Key Points | + | == '''Key Points''' == |
The moment of the force about the point O is the product of the force and the perpendicular distance to the line of action of the force from O. | The moment of the force about the point O is the product of the force and the perpendicular distance to the line of action of the force from O. | ||
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[[Image:T13.1.GIF]] | [[Image:T13.1.GIF]] | ||
<math>\text{Moment }=Fd</math> | <math>\text{Moment }=Fd</math> | ||
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[[Image:T13.2.GIF]] | [[Image:T13.2.GIF]] | ||
<math>\text{Moment }=Fd\sin \theta </math> | <math>\text{Moment }=Fd\sin \theta </math> | ||
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Clockwise moments are negative. | Clockwise moments are negative. | ||
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Anti-clockwise moments are positive. | Anti-clockwise moments are positive. | ||
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[[Image:ex13.1whole.GIF]] | [[Image:ex13.1whole.GIF]] | ||
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For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O. | For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O. | ||
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[[Image:ex13.3.GIF]] | [[Image:ex13.3.GIF]] | ||
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{| width="100%" cellspacing="10px" align="center" | {| width="100%" cellspacing="10px" align="center" | ||
|align="left"| Force | |align="left"| Force | ||
| - | | valign="top"|Moment | + | | valign="top"|Moment (Nm) |
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|5N at O | |5N at O | ||
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|valign="top"| <math>-8\times 1\textrm{.}2=-9\textrm{.}6</math> | |valign="top"| <math>-8\times 1\textrm{.}2=-9\textrm{.}6</math> | ||
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|7 N | |7 N | ||
| valign="top"| <math>7\times 0=0</math> | | valign="top"| <math>7\times 0=0</math> | ||
Revision as of 10:29, 17 February 2010
| Theory | Exercises |
Key Points
The moment of the force about the point O is the product of the force and the perpendicular distance to the line of action of the force from O.
\displaystyle \text{Moment }=Fd
\displaystyle \text{Moment }=Fd\sin \theta
Clockwise moments are negative.
Anti-clockwise moments are positive.
For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.
Solution
| Force | Moment (Nm) |
| 5N at O | \displaystyle 5\times 0=0 |
| 8 N | \displaystyle -8\times 1\textrm{.}2=-9\textrm{.}6 |
| 7 N | \displaystyle 7\times 0=0 |
| 6 N | \displaystyle -6\times 0\textrm{.}5=-3 |
| 5 N | \displaystyle 5\times 1\textrm{.}2=6 |
| 4 N | \displaystyle 4\times 0\textrm{.}5=2 |
| Total Moment | \displaystyle 0-9\textrm{.}6+0-3+6+2=-4\textrm{.}6\text{ Nm} |
