13. Moments
From Mechanics
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| - | {{Selected tab|[[13. Moments|Theory]]}} | + | {{Selected tab|[[13. Moments|Theory]]}} |
{{Not selected tab|[[13. Exercises|Exercises]]}} | {{Not selected tab|[[13. Exercises|Exercises]]}} | ||
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| + | == '''Key Points''' == | ||
| - | + | The moment of a force about the point <math>O</math> is the product of the force and the perpendicular distance to the line of action of the force from <math>O</math>. | |
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| - | The moment of | + | |
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[[Image:T13.1.GIF]] | [[Image:T13.1.GIF]] | ||
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<math>\text{Moment }=Fd</math> | <math>\text{Moment }=Fd</math> | ||
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[[Image:T13.2.GIF]] | [[Image:T13.2.GIF]] | ||
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<math>\text{Moment }=Fd\sin \theta </math> | <math>\text{Moment }=Fd\sin \theta </math> | ||
| + | Clockwise moments are negative. | ||
| - | Clockwise moments are negative. | ||
Anti-clockwise moments are positive. | Anti-clockwise moments are positive. | ||
| + | The resultant moment about <math>O</math> is the sum of the moments about <math>O</math>. | ||
| - | Example 13.1 | + | |
| + | '''[[Example 13.1]]''' | ||
[[Image:ex13.1whole.GIF]] | [[Image:ex13.1whole.GIF]] | ||
| + | '''[[Example 13.2]]''' | ||
| + | [[Image:ex13.2.GIF]] | ||
| - | + | '''[[Example 13.3]]''' | |
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| - | [[ | + | |
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| - | Example 13.3 | + | |
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]] | ||
| - | Solution | + | '''Solution''' |
{| 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) |
|- | |- | ||
| - | |5N at O | + | |5N at <math>O</math> |
| valign="top"| <math>5\times 0=0</math> | | valign="top"| <math>5\times 0=0</math> | ||
|- | |- | ||
|8 N | |8 N | ||
| - | |valign="top"| <math>-8\times 1.2=-9.6</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> | ||
|- | |- | ||
|6 N | |6 N | ||
| - | | valign="top"| <math>-6\times 0.5=-3</math> | + | | valign="top"| <math>-6\times 0\textrm{.}5=-3</math> |
|- | |- | ||
|5 N | |5 N | ||
| - | | valign="top"| <math>5\times 1.2=6</math> | + | | valign="top"| <math>5\times 1\textrm{.}2=6</math> |
|- | |- | ||
|4 N | |4 N | ||
| - | | valign="top"| <math>4\times 0.5=2</math> | + | | valign="top"| <math>4\times 0\textrm{.}5=2</math> |
|- | |- | ||
|Total Moment | |Total Moment | ||
| - | | valign="top"| <math>0-9.6+0-3+6+2=-4.6\text{ Nm}</math> | + | | valign="top"| <math>0-9\textrm{.}6+0-3+6+2=-4\textrm{.}6\text{ Nm}</math> |
|} | |} | ||
Current revision
| Theory | Exercises | Video |
Key Points
The moment of a force about the point \displaystyle O is the product of the force and the perpendicular distance to the line of action of the force from \displaystyle O.
\displaystyle \text{Moment }=Fd
\displaystyle \text{Moment }=Fd\sin \theta
Clockwise moments are negative.
Anti-clockwise moments are positive.
The resultant moment about \displaystyle O is the sum of the moments about \displaystyle O.
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 \displaystyle 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} |
