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Encyclopedia Britannica



AHK

This article appears in Volume V17, Page 974 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: ADA-AIZ
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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