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Section 4.1 Direction of a Moment

In a two-dimensional problem the direction of a moment can be determined easily by inspection as either clockwise or counter-clockwise. A counter-clockwise rotation corresponds with a moment vector pointing out of page and is considered positive.

In three-dimensions a moment vector may point in any direction in space and is more difficult to visualize. The direction is established by the right hand rule.

To apply the right hand rule, first establish a a position vector \(\vec{r}\) pointing from the rotation center to the point of application of the force, or another point on its line of action. If you align your thumb with the position vector and your index finger with the force vector, then your middle finger points the direction of the moment vector \(\vec{M}\text{.}\) Alternately, you can align your index finger with the position vector and your middle finger with the force vector, and your thumb will point in the direction of the moment vector.

Figure 4.1.1. Two ways to apply the right hand rule to determine the direction of a moment.

Another approach is the point-and-curl method. Start with your hand flat and fingertips pointing along the position vector \(\vec{r}\) pointing from the center of rotation to a point on the force’s line of action. Adjust your hand so the force vector \(\vec{F}\) pushes fingers into a curl. Your thumb then defines the direction of the moment \(\vec{M}\text{.}\)

Figure 4.1.2. Point-and-curl right-hand rule technique for moments.

Any of these techniques may be used to find the direction of a moment. They all produce the same result so you don’t need to learn them all, but make sure you have at least one method you can use accurately and consistently.