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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Key Points
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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]]
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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>
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Clockwise moments are negative.
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Clockwise moments are negative.
 
Anti-clockwise moments are positive.
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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'''[[Example 13.1]]'''
[[Image:ex13.1whole.GIF]]
[[Image:ex13.1whole.GIF]]
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Find the moment of each force shown below about the point O.
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'''[[Example 13.2]]'''
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[[Image:ex13.1.GIF]]
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Solution
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(a)
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<math>20\times 0.8=16</math>
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Moment is -16 Nm
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(b)
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<math>12\times 1.2=14.4</math>
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Moment is 14.4 Nm
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Example 13.2
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[[Image:ex13.2.GIF]]
[[Image:ex13.2.GIF]]
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Find the moment of each force shown below about the point O.
 
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(a) (b)
 
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'''[[Example 13.3]]'''
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Solution
 
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(a) (b)
 
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<math>40\times 3\sin 60{}^\circ =104</math>
 
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<math>100\times 2\sin 20{}^\circ =68.4</math>
 
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Moment is 104 Nm (to 3 sf) Moment is 68.4 Nm (to 3 sf)
 
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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]]
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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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|}
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Solution
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Force Moment
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5N at O
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<math>5\times 0=0</math>
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8 N
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<math>-8\times 1.2=-9.6</math>
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7 N
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<math>7\times 0=0</math>
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6 N
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<math>-6\times 0.5=-3</math>
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5 N
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<math>5\times 1.2=6</math>
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4 N
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<math>4\times 0.5=2</math>
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Total Moment
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<math>0-9.6+0-3+6+2=-4.6\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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