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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