1. Lecture# 12: Rigid Bodies
Rigid Body:
For system where forces are not concurrent
Coplanar Force System, Parallel Force System
Non-concurrent etc. F1 F3 F2
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2. Equilibrium: Section 4.1 Necessary Conditions are:
Important the Point where forced is apply may rotate the body. P P
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3. Moments: Tendency of Force to rotate the body.
Moment is a Vector: Magnitude + direction
d moment arm, o moment center, F d F d o o d F
direction
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4. Can all Forces Produce Moment?
Which of Forces produce moment about point o. y F3 F2 x o F1 d1 d2
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5. Activity #1: Find the moment of F1 about point A.
Also, indicate direction of moment. y
F1=8KN A x 3m
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6. Activity #2: Find the moment of F1 & F2 about point A.
Also, indicate direction of moment. y
F1=8KN
F2=3KN
60o A x 3m 6m
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7. Summary: Moment is a vector: mag. + dir.
Forces that passes through point of interest Mo=0.
Also, Forces Parallel to point o Mo=0.
Direction indicated by: clocwise (-), counter clockwise (+)
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8. Section 4.2: Varignon’s Theorem
The moment, M, of the Resultant force, R, is equal to the sum of the moments created by each single force.
NOTE: ALL moments are taken at same point.
Mo = RdR = F1d1 + F2d2 + F3d3 +….+Fndn
Sign Convention for Moments:
(+) counter clockwise
(-) clockwise
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9. Example #2: Find the moment of F1 about point A.
Also, indicate direction of moment. y
F2=3KN 2m
60o A x 6m
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10. Activity #3: Determine the moment of 250N force about point A. y
250mm
210mm
32o x
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11. Example #3: (a) Find the moments of FA and Fc about point o.
(b) Find moment of Force FB about point D.
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12. Activity #4: (a) Find the moments of FA and Fc about point C.
(b) Find moment of Force FB about point o.
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