Online Encyclopedia

AHK

Online Encyclopedia
Originally appearing in Volume V17, Page 974 of the 1911 Encyclopedia Britannica.
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AHK, that of the second by twice the area BKL, and so on. The quadratic moment of the whole system is there-fore represented by twice the area AHEDCBA. Since a quadratic moment is essentially positive, the various areas are to taken positive in all cases. If k be the radius of gyration about p we find k2 =2 X area AHEDCBA X ON 4- aP, where a¢ is the line in the force-diagram which represents the sum of the masses, and ON is the distance of the pole 0 from this line. If some of the particles lie on one side of p and some on the other, the quadratic moment of each set may be found, and the results added. This is illustrated in fig. 6o, where the total quadratic '~miIIIII~~~ii~~~II~IIII~IIIIpII~I P moment is represented by the sum of the shaded areas. It is seen that for a given direction of p this moment is least when p passes through the intersection X of the first and last sides of the funicular; i.e. when p goes through the mass-centre of the given system; cf. equation (15). -
End of Article: AHK
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