13. Moment

Förberedande Mekanik

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Rad 9: Rad 9:
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Key Points
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== '''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.
Rad 33: Rad 30:
[[Image:ex13.1whole.GIF]]
[[Image:ex13.1whole.GIF]]
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Rad 46: Rad 40:
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]]
Rad 54: Rad 47:
{| width="100%" cellspacing="10px" align="center"
{| width="100%" cellspacing="10px" align="center"
|align="left"| Force
|align="left"| Force
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| valign="top"|Moment
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| valign="top"|Moment (Nm)
|-
|-
|5N at O
|5N at O
Rad 62: Rad 55:
|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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|-
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|7 N
|7 N
| valign="top"| <math>7\times 0=0</math>
| valign="top"| <math>7\times 0=0</math>

Nuvarande version

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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.

Image:T13.1.GIF

\displaystyle \text{Moment }=Fd

Image:T13.2.GIF

\displaystyle \text{Moment }=Fd\sin \theta

Clockwise moments are negative.

Anti-clockwise moments are positive.


Example 13.1

Image:ex13.1whole.GIF


Example 13.2

Image:ex13.2.GIF


Example 13.3

For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.

Image:ex13.3.GIF

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}
Den här artikeln är hämtad från http://wiki.sommarmatte.se/wikis/2010/forberedandemekanik/index.php/13._Moment