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13. Moments

From Mechanics

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[[Image:T13.GIF]]
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[[Image:T13.1.GIF]]
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<math>\text{Moment }=Fd</math> <math>\ \ \ \ \ \ \ \ \ \text{Moment }=Fd\sin \theta </math>
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<math>\text{Moment }=Fd</math>
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Clockwise moments are negative.
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[[Image:T13.2.GIF]]
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Anti-clockwise moments are positive.
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<math>\text{Moment }=Fd\sin \theta </math>
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Example 11.1
 
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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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Clockwise moments are negative.
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Anti-clockwise moments are positive.
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Example 13.1
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[[Image:ex13.1whole.GIF]]
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Find the moment of each force shown below about the point O.
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[[Image:ex13.1.GIF]]
Solution
Solution
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(a) (b)
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(a)
<math>20\times 0.8=16</math>
<math>20\times 0.8=16</math>
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<math>12\times 1.2=14.4</math>
 
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Moment is -16 Nm
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Moment is -16 Nm Moment is 14.4 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
Example 13.2
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[[Image:ex13.2.GIF]]
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Find the moment of each force shown below about the point O.
Find the moment of each force shown below about the point O.
(a) (b)
(a) (b)

Revision as of 19:09, 17 September 2009

       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

Find the moment of each force shown below about the point O.


Image:ex13.1.GIF

Solution

(a)

2008=16

Moment is -16 Nm


(b)

1212=144

Moment is 14.4 Nm


Example 13.2

Image:ex13.2.GIF

Find the moment of each force shown below about the point O. (a) (b)




Solution (a) (b)






403sin60=104

1002sin20=684


Moment is 104 Nm (to 3 sf) Moment is 68.4 Nm (to 3 sf)

Example 13.3 For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.






Solution

Force Moment 5N at O 50=0

8 N −812=−96

7 N 70=0

6 N −605=−3

5 N 512=6

4 N 405=2

Total Moment 0−96+0−3+6+2=−46 Nm

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