4: Moments and Static Equivalence

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When a force is applied to a body, the body tends to translate in the direction of the force and also tends to rotate. We have already explored the translational tendency in Chapter 3. We will focus on the rotational tendency in this chapter.

This rotational tendency is known as the moment of the force, or more simply the moment. You may be familiar with the term torque from physics. Engineers use “torque” where physicists use “moment” to describe the same concept. Moments are vectors, so they have magnitude and direction and obey all rules of vector addition and subtraction described in Chapter 2. Additionally, moments have a center of rotation, although it is more accurate to say that they have an axis of rotation. In two dimensions, the axis of rotation is perpendicular to the plane of the page and so will appear as a point of rotation, also called the moment center. In three dimensions, the axis of rotation can be any direction in 3D space.

A wrench provides a familiar example. A force \(\vec{F}\) applied to the handle of a wrench, as shown in Figure 4.0.1, creates a moment \(\vec{M}_A\) about an axis out of the page through the centerline of the nut at \(A\text{.}\) The \(\vec{M}\) is bold because it represents a vector, and the subscript \(A\) indicates the axis or center of rotation. The direction of the moment can be either clockwise or counter-clockwise depending on how the force is applied.

This interactive shows how a force \(\vec{F}\) causes a moment \(\vec{M}_A\) around point \(A\text{.}\) Rotate the the wrench and force \(\vec{F}\) to see how the magnitude of the moment changes.

Figure 4.0.1. A moment \(\vec{M}_A\) is created by force \(\vec{F}\text{.}\)