Mechanics of Engineering and Machinery Volume 1

Mechanics of Engineering and Machinery Volume 1

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 edition. Excerpt: ...of inertia is to be determined; let S D = d be the distance between the two axes and S JV, = xx and JV, M, = y, the rectangular co-ordinates of an element M, of the mass of the whole body. The moment of inertia of this element in reference to D will be But Jf, + M, +... is the sum M of all the masses and Mx + 3f2 a:, + Mx xs is the sum M x of the statical moments; hence it follows that the difference between the moment of inertia IF, of the whole body in reference to the axis D and its moment of inertia W in reference to S is IF, -W= MT + 2dMx. But since the sum of the statical moments of all the elements upon one side of every plane passing through the centre of gravity is equal to that of the moment of those on the other, the algebraical sum of all the moments is = 0, and we have M x--0, and consequently W, -W=McP, I.e JF, = IF + ATcT. The moment of inertia of a body in reference to an eccentric axis is equal to the moment of inertia in reference to a parallel axis passing through the centre of gravity plus the product of the mass of the body by the square of the distance of the two axes from each other. We see from this that of all the moments of inertia in reference to a set of parallel axes that one is the least, whose axis is a line of gravity of the body. 285. Radius of Gyration.--It is very important to determine the moment of inertia for various geometrical bodies; for the values thus deduced are frequently employed in the different calculations in mechanics. If the bodies, as we will hereafter suppose, are homogeneous, the different portions Mlf M etc., of the mass, are proportional to the corresponding portions V V etc., of the volume, and the measure of the moment of inertia, or as it is generally called, more

Product details

  • Paperback | 260 pages
  • 189 x 246 x 14mm | 472g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236538854
  • 9781236538857