By Jon Fridjonsson
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Extra resources for Course in Modern Icelandic
3-1-3-15] PARALLELOGRAM OF FORCES 13 inasmuch as a force is a vector localized in a line due care must be exercised in order to determine in what line the resultant force is localized. This determination is embodied in the proposition known as the Parallelogram of Forces, which states that: If two forces acting at a point are represented in magnitude and direction by the sides of a parallelogram drawn from that point, then their resultant is represented by the diagonal of the parallelogram drawn from that point.
The algebraical sum of the moments of any number of coplanar forces which meet at a point about a point on the line of action of their resultant is zero. 4*21. The Moment of a Force about a Line is defined to be the product of the resolved part of the force at right angles to the line and the shortest distance between the force and the hne. Thus if P be a force and Oz be a line which does not intersect P, MN=p the shortest distance between P and Oz, and N Psinfl 8 the angle between P and a hne through M parallel to Oz, then P sin 6 is the resolved part of P at right angles to Oz and Pp sin 8 is the moment of P about Oz.
4*6. Couples. Couples play an important part in the general theory of systems of forces and we shall now establish some of their principal properties. Since a couple consists of two equal and opposite parallel forces, the algebraical sum of the resolved parts of the forces in every direction is zero, so that there is no tendency for the couple to produce in any direction a displacement of translation of the body upon which it acts; and, as we saw in 4*31, the couple cannot be replaced by a single force.
Course in Modern Icelandic by Jon Fridjonsson