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. 1886 Excerpt: ...of Plane Figures ( 85).--Since the axis is now perpendicular to the plane of the figure, intersecting it in a point, 0, the distances of the elements of ai-ea will all radiate from this point, and would better be denoted by p instead of z; hence, Fig. 109, fp'dF is the polar moment of inertia of any plane figure about ...
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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. 1886 Excerpt: ...of Plane Figures ( 85).--Since the axis is now perpendicular to the plane of the figure, intersecting it in a point, 0, the distances of the elements of ai-ea will all radiate from this point, and would better be denoted by p instead of z; hence, Fig. 109, fp'dF is the polar moment of inertia of any plane figure about a specified point 0; this may be denoted by Ip. But p' Fio. 109. = '-(-ya, for each dF; hence Iv =M + y')dF=fx'dF+fy'dF= 1T+ Ix. i.e., the polar moment of inertia about any given point in the plane equals the sum of the rectangular moments of inertia about any two axes of the plane figure, which intersect at right angles in the given point. We have therefore for the circle about its centre Ip = nr + ir = nrK; For a ring of radii r, and r, h = ir: -O; For the rectangle about its centre, I, =-hbh' + &hb' = bhV + A'); For the square, this reduces to rP = W (See 90 and 91.) 95. Slender, Prismatic, Homogeneous Rod.--Keturning to the moment of inertia of rigid bodies, or solids, we begin with that of a material line, as it might be called, about an axis through its extremity making some angle a with the rod. Let I--length of the rod, O. iits cross-section (very small, the result being K.-'" strictly true only when F = 0). Subdivide Fio. no. the rod into an infinite number of small prisms, each having F n& a base, and an altitude--ds. Let y = the heaviness of the material; then the mass of an elementary prism, or dM, = (y g)Fds, while its distance from the axis Z is p = s sin a. Hence the moment of'inertia of the rod with respect to Z as an axis is Iz = f p'dM = (y + g)Fsn' ctjs'ds = i(y g)FV But yFl g = mass of rod and I sin a = a, the distance of the further extremity from the axis; hence Iz = Ma' an...
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Add this copy of Statics and Dynamics for Engineering Students to cart. $18.00, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
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Add this copy of Statics and Dynamics for Engineering Students to cart. $41.38, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
