By F. Seely, N. Ensign [non-OCR]
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Additional resources for Analytical Mechanics for Engineers
Applying to a system of parallel forces in a plane the principle As may be stated formally as follows The algebraic sum of the moments of the forces of a coplanar parallel system about any point in their plane is equal to the moment of the resultant of the system about the same : point. In demonstrating the truth of this statement use will be made of the diagram in Fig. 35 and of the methods of the preceding article. The given system of four forces (Fig. 35) was replaced by another system of eight forces which were represented in magnitude and by the rays of the force polygon and in line of action in direction by the strings of the funicular polygon.
Presses a measure of the tendency of the force to turn the body on which it acts about a given axis. ^ Strictly speaking, the fact that the tendency of a force to turn a body about a given , axis is directly proportional assumption which, of observed ysis crystallizes when to the reinforced moment by of the force, is an experience and the anal- facts, into a fun- damental or basic truth of mechanics. In general, the moof a force about ment an axis which perpendicular is not to the plane of the force is defined as the the moment component of of the force perpendicular to the given axis, the other component of the force being Fig.
General a sum, difference, product, or quotient of two approximate values will not have a greater degree of accuracy than that of the least accurate of the two numbers. For example, if one numerical quantity is accurate to two significant figures and another quantity to three significant figures, the product of the two numbers will not be accurate to more than two significant figures, and hence more than two significant figures should not be retained in the result. Dimensional Equations. In algebraic equations in which the variables represent physical quantities, all of the terms of the equation must be of the same dimensions, or, to express the same mathematical language, an algebraic equation which expresses a relation between physical quantities must be homogeneous.