Begin2.DVI

Construct the vector r 0 −r 1 which points from the terminus of r 1 to the terminus of

r 0 and construct the unit normal to the plane which is given by

ˆeN=N^1 √eˆ^1 +N^2 eˆ^2 +N^3 ˆe^3 N 12 +N 22 +N 32

Observe that the dot product eˆN·(r 0 −r 1 )

equals the projection of r 0 −r 1 onto ˆeN. This

gives the distance

d=|ˆeN·(r 0 −r 1 )|=

∣∣ ∣∣ ∣

(x 0 −x 1 )N (^1) √+ (y 0 −y 1 )N 2 + (z 0 −z)N 3
N 12 +N 22 +N 32
∣∣
∣∣
∣

where the absolute value signs guarantee that the

sign of dis always positive and does not depend

upon the direction selected for the unit vector ˆeN.

Moment Produced by a Force

The moment of a force with respect to a line is a measure of the forces tendency

to produce a rotation about the line. Let a force F acting at the point (x 1 , y 1 , z 1 )

be resolved into components parallel to the coordinate axes by expressing F in the

component form

F=F 1 ê 1 +F 2 ê 2 +F 3 ê 3

That component of the force which is parallel to an axis has no tendency to produce a

rotation about that axis. For example, the F 1 component is parallel to the x−axis and

does not produce a rotation about this axis. For a chosen axis, the moment about

that axis is the product of the force component times the perpendicular distance of

the force from the axis. By using the right-hand screw rule, one can assign a negative

sign to the moment if it acts clockwise and a positive sign to the moment if it acts

counterclockwise. The moment of a force is a vector quantity which produces a

definite sense of rotation about an axis.

With the use of figure 6-12 let us calculate the moment of a force F, acting at

the point (x 1 , y 1 , z 1 ), about the x-, y- and z-axes.

(a) For the moment about the x-axis produces

F 1 component parallel to x-axis does not produce moment

(Force)(⊥distance) = + F 3 y 1 (Counterclockwise rotation)

(Force)(⊥distance) =−F 2 z 1 (Clockwise rotation)