Section 2.3 Solid Mechanics Part I Kelly 172.3 The Statics of Rigid Bodies A material body can be considered to consist of a very large number of particles. A rigid body is one which does not deform, in other words the distance between the individual particles making up the rigid body remains unchanged under the action of external forces. A new aspect of mechanics to be considered here is that a rigid body under the action of a force has a tendency to rotateabout some axis. Thus, in order that a body be at rest, one not only needs to ensure that the resultant force is zero, but one must now also ensure that the forces acting on a body do not tend to make it rotate. This issue is addressed in what follows. 2.3.1 Moments, Couples and Equivalent Forces When one swings a door on its hinges, it will move more easily if (i) one pushes hard, i.e. if the force is large, and (ii) if one pushes furthest from the hinges, near the edge of the door. It makes sense therefore to measure the rotational effect of a force on an object as follows: The tendency of a force to make a rigid body rotate is measured by the momentof that force about an axis. The moment of a force Fabout an axis through a point o is defined as the product of the magnitude of Ftimes the perpendicular distance dfrom the line of actionof Fand the axis o. This is illustrated in Fig. 2.3.1. Figure 2.3.1: The moment of a force F about an axis o (the axis goes “into” the page) The moment oMof a force Fcan be written as FdM=0(2.3.1) Not only must the axis be specified (by the subscript o) when evaluating a moment, but the sense of that moment must be given; by convention, a tendency to rotate counterclockwiseis taken to be a positivemoment. Thus the moment in Fig. 2.3.1 is positive. The units of moment are the Newton metre (Nm) Note that when the line of action of a force goes through the axis, the moment is zero. d•Rigid body •oFline of action of force axispoint of application of force
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