Moment of a force

The concept of moments was adopted in statistics from the science of mechanics where it was first used in the sense of importance. The moment of a force about an axis meant the importance of the force in causing rotation about the axis. Similarly, the moment of inertia of a body with respect to an axis expressed the importance of the inertia of the body in resisting a change in the rate of rotation of the body about the axis. 

The first moment of a force or weight about an axis is defined as the product of the force and the distance from the axis to the line of action of the force. In this case it is commonly known as the torque. The concept has been extended to more abstract applications such as the moment of an area with respect to a plane and moments of statistical distributions. It is then referred to as the appropriate first moment (the term torque is not used). 

In this analysis the moment of a force with respect to an axis, namely, torque, is important. Although the linear momentum equation can be used to solve problems involving torques, it is generally more convenient to apply the angular moment equation for this purpose. By forming the moment of the linear momentum and the resultant force associated with each particle of fluid with respect to a point in an inertial coordinate system, a moment of moment equation that relates torque and angular momentum flow can be obtained. 

ANGULAR-MOMENTUM EQUATION. Analysis of the performance of rotating fluid-handling machinery such as pumps, turbines, and agitators is facilitated by the use of force moments and angular momentum. The moment of a force F about point 0 is the vector product of F and the position vector r of a point on the line of action of the vector from 0. When a force, say Fg, acts at right angles to the... 

A moment in mechanics is generally defined as Uj = Qd, where Uj is the jth moment, about a specified line or plane a of a vector or scalar quantity Q (e.g., force, weight, mass, area), d is the distance from Q to the reference line or plane, and j is a number indicating the power to which d is raised. [For example, the first moment of a force or weight about an axis is defined as the product of the force and the distance of the fine of action of the force jfrom the axis. It is commonly known as the torque. The second moment of the force about the same axis (i.e., i = 2) is the moment of inertia.] If Q has elements Qi, each located a distance di from the same reference, the moment is given by the sum of the individual moments of the elements ... 

The tQvm moment comes from mechanics. The first moment of a force is defined as the product of the force (e.g., g) and the distance (e.g., E) along the axis from the point of application of the force. The second moment is... 

Also note that the reason this property of an area is called second moment of area is that the definidon contains the product of distance squared and an area, hence the name second moment of area. In Chapter 10, we will discuss the proper definidon of a moment and how it is used in relation to the tendency of unbalanced forces to rotate things. As you will learn later, the magnimde of a moment of a force about a point is determined by the product of the perpendicular distance from the point about which the moment is taken to the line of acdon of the force and the mj itude of that force. You have to pay attendon to what is meant by a moment of a force about a point or an axis and the way the term moment Is incorporated into the name the second moment of area or the area moment of inertia. Because the distance term is multiplied by another quantity (area), the word moment appears in the name of this property of an area. 

In this book, we will only consider the moment of a force about a point. Most of you will take a mechanics chiss, where you will learn how to calculate the magnitude and the direcdon of moment of a force about an arbitrary axis. For an object that is subject to force F, the relationship between the line of acxion of the force and momem arm is shown in Figure 10.22. The magnitude of moment about arbitraty points B, and C is given by... 

In the same way as when reading, it is helpful to think about the topic of a lecture before you listen. The topic here is The Moment of a Force. Can you explain the links between these words from the lecture and the topic Use a dictionary to help you if necessary. 

The moment of a force is equal to the product of the force and the perpendicular distance from the... 

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