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13. Moments

From Mechanics

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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.
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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
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| valign="top"|Moment
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| valign="top"|Moment (Nm)
|-
|-
|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.

Image:T13.1.GIF

Moment =Fd

Image:T13.2.GIF

Moment =Fdsin

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 50=0
8 N −81.2=−9.6
7 N 70=0
6 N −60.5=−3
5 N 51.2=6
4 N 40.5=2
Total Moment 0−9.6+0−3+6+2=−4.6 Nm
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