The view from the y axis reveals that is perpendicular to the x axis and that its line of action does not intersect the x axis. Thus, the moment of around the x axis isdiscovered as

*

wright here

*
is the momentarm of the pressure with respect to the x axis. In this situation, themoment axis is pointing in the positive x direction as presented.Similarly, the see from the x axisreveals that isperpendicular to the y axis as well. Hence, the moment of about the y axis isuncovered as

*
*
where
*
is the momentarm of the force via respect to the y axis. In this situation, theminute axis is pointing in the negative y direction. Also regarding bemeant,
*
given that is parallel to the zaxis.

You are watching: Moment of a force about a line

We deserve to currently expand also this discussion to the case of calculating themoment around an arbitrary line aa. Twogenerally encountered instances are explained next.


Case 1: The line of activity of the forceis perpendicular to aa, and that the twolines execute not intersect each various other.

In this situation, the minute about aa isfound as

*
(6)

An instance of this situation is shown in the number wbelow the line ofaction of the force is in z direction and also line aa is in xy plane; clearly, they areperpendicular to each other.

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*
Case 2: The line of activity of the forceis NOT perpendicular to aa, and also that thetwo lines do not intersect each various other.

In this situation, the minute about aa isdiscovered in 2 measures using the vector approach. First, the momentaround a point lying on line aa iscalculated as

*

Then, the forecast of

*
alengthy line aa is discovered usingthe dot product

*
(Magnitude of the component)

*
The previous two equations can be linked into a triple scalarproduct as

*
(7)
If
*
comes out negative, it simply means that its direction is oppositeto that defined by
*
This forecast can likewise be put in vector create as