Page 23 - mechanics
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Chapter – 4       Non-Concurrent forces and Moments

about an axis can be obtained by evaluating the moment vector

of the force about a point on that axis then determining its

component (projection) along the axis direction. This is a

known application of dot product of vectors. Let O be a point

that belongs to the moment axis AB. Then,

                  M AB = MO  uAB .                        (4.10)

Where MO = r  F

So, the above two equations can be combined to determine the

moment of a force F about an axis AB in a one step formula

using the mixed triple product as

                  M AB = (r  F)  uAB                     (4.11)

and as it is directed along AB, i.e. the moment parallel

component to axis AB, then its vector form is obtained by

                  MAB = M AB uAB                           (4.12)

Indeed this implies that there exists a perpendicular moment

component to axis AB obtained by

                  M⊥ = Mo − MAB                            (4.13)

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