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Engineering Statics: Open and Interactive

Chapter 4 Moments and Static Equivalence

When a force acts on a body, it can potentially produce two effects: translation of the body in the direction of the force, and rotation of the body about an axis. For a body in equilibrium we say that forces have a tendency to produce translation or rotation since no actual acceleration or motion occurs.
The rotational tendency of a force is the subject of this chapter. Engineers call this rotational tendency a moment, short for “moment of a force.” You may remember the using the term torque for the same quantity in physics. Physicists use torque specifically for a moment of a force, and moment for the product of any physical quantity with distance. To an engineer, a torque means a moment about the long axis of an object that produces twisting and torsional stresses.
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 perpendicular to the page through the center of the nut at \(A\text{.}\) The \(\vec{M}\) is bold because moments are vector quantities, 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. If the nut is frozen, no actual rotation occurs, but the force still produces a tendency to rotate it, i.e. a moment.


This interactive shows how a force \(\vec{F}\) causes a moment \(\vec{M}_A\) around point \(A\text{.}\) Rotate 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 about point \(A\) by force \(\vec{F}\text{.}\)