Wize University Statics Textbook (Master) > Force System Resultants (Moment, Couple, Dist. Load)

MOMENT (M):
aka Moment of Force,  means "moving power"
is arises when a FORCE acts at a distance from a POINT or AXIS to cause ROTATION
measure of the tendency of force to cause body to rotate about a point or axis
is similar to the term Torque or Twist from Physics 1 classes
if MORE THAN 1 MOMENT on the body, then must Sum M's (like we Sum F's earlier)
FORCE vs. MOMENT:
Forces tend to cause translation of an object (Newton's 2nd Law, F = m a)
Moments tend to cause rotation (Newton's 2nd Law for Rotational Motion, T = I w). 
in 2D 
about a point, z-axis out of page
M = F d      or     M = F d sin(theta)
M represented by CCW "curl" using Right-Hand-Rule
thinking of a SEE-SAW, the rider on the LEFT would cause a CCW moment, the rider on the RIGHT would cause a CW moment.  we would need to Sum M's to see which direction it will rotate.

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in 3D :  
about a point or line or axis
M = r x F   (cross product, it will handle the angle)
M represented by "curl with vector arrow pointing in the direction of the line/axis" using Right-Hand-Rule

Determine the moment of the force F=80 lb about the base A created by the work at C.

in 2D: M = F d
Ma = Fx (12') + Fy (0')
       = 80 (4/5)(12') = 768 lb ft CW

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Determine the moment of the force P=50 lb about the base A created by the work at B.

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If Fb = [3j-4k] kN, find the moment about the base O.

in 3D, the Moment vector M = r x F
F = [3j-4k] kN
building the position vector r using points A and O, results in:
r = [0i + 0j + 8k]m

taking the cross product:
|    i     j     k   |
|   0    0    8   |      =    [(0)(-4)-(8)(3)]i - [(0)(-4)-(8)(0)]j + [(0)(3)-(0)(0)]k
|   0    3   -4  |

                             = [ -24i ] kNm

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If FCD = [2i-3j-6k] kN, find the moment about the base O due to just this force.

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