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13. Moments

From Mechanics

Revision as of 19:09, 17 September 2009 by Ian (Talk | contribs)
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       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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