13. Moments

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== '''Key Points''' ==
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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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[[Image:T13.1.GIF]]
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<math>\text{Moment }=Fd</math>
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[[Image:T13.2.GIF]]
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<math>\text{Moment }=Fd\sin \theta </math>
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Clockwise moments are negative.
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Anti-clockwise moments are positive.
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The resultant moment about <math>O</math> is the sum of the moments about <math>O</math>.
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'''[[Example 13.1]]'''
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[[Image:ex13.1whole.GIF]]
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'''[[Example 13.2]]'''
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[[Image:ex13.2.GIF]]
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'''[[Example 13.3]]'''
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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]]
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'''Solution'''
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{| width="100%" cellspacing="10px" align="center"
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|align="left"| Force
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| valign="top"|Moment (Nm)
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|-
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|5N at <math>O</math>
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| valign="top"| <math>5\times 0=0</math>
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|-
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|8 N
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|valign="top"| <math>-8\times 1\textrm{.}2=-9\textrm{.}6</math>
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|-
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|7 N
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| valign="top"| <math>7\times 0=0</math>
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|-
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|6 N
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| valign="top"| <math>-6\times 0\textrm{.}5=-3</math>
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|-
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|5 N
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| valign="top"| <math>5\times 1\textrm{.}2=6</math>
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|-
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|4 N
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| valign="top"| <math>4\times 0\textrm{.}5=2</math>
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|-
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|Total Moment
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| valign="top"| <math>0-9\textrm{.}6+0-3+6+2=-4\textrm{.}6\text{ Nm}</math>
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|}
|}

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.

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.

The resultant moment about \displaystyle O is the sum of the moments about \displaystyle O.


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 \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}
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