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. 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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6. Summary: Moment is a vector: mag. + dir.
Forces that passes through point of interest Mo=0.
Direction indicated by:
clocwise (-)
counter clockwise (+)
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7. Vector Product of two vectors
Vector Product of r and F must satisfy:
Mo is perpendicular to plane of r & F.
Magnitude of Mo given by.
Direction:
right-hand rule: o
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8. Sec. 4.3: Vector Representation of a Momentz
Fzk
Fyj r
Fxi o y x
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9. Vector Product in 3-D Space
Moment about a point o. z o y x
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10. Components of Mo: The three components Determinant of above matrix:
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11. Magnitude & Direction of Mo:
Direction given by unit Vector e:
where
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12. Example #1:
Do problem in a 2-D space using above method.
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13. Activity #1: Determine the moment of the force 760 lb about point A. y
ANS:=11,871 in.lb ccw y
760
12in
40o x
10in
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14. Example #2: 3D Space Find: (a) Moment about Mo (b) Magnitude of Mo.
© Direction of Mo.
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15. Activity#2 & #3 For following problem find (a) Mo=? (b) Magnitude Mo=?
(c ) Direction =?
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16. MAple Matrix A:=[x,y,z] Mag:= evalf(sqrt(dotprod(A,A)))
Matrix B:=[x,y,z]
AXB:= crossprod(A,B);
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