Forces and Moments – continued - (Vectors)

Calculate the moment, M, of force, F, about point P but directed along

the line, L – L.

Strategy: Calculation of the moment of a force about a line is a two-step process.

First calculate the moment of the force about any point, P. Then calculate the

the component of the moment directed along the line L – L using the dot product

to get the component of the moment along the line.

M = ( r sin θ) F = | r x F | Note r sin θ is perpendicular distance from point P

to point Q on the line of action of the force F.

So the moment of the force, F, about point P is M = r x F

in English units the moment has units of lb ft and in Metric units Nm.

Suppose the direction of the line L – L is defined by the vector, V = a i + b j + c k

where i, j, and k are unit vectors along the x, y, and z axes respectively. Then the

unit vector along line L – L is just u = V / V where V = √ ( a² + b² + c² )

The result for the moment of the force, F, about line L – L is then

M = ( r x F ) ● u

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