 Expressed in words, this equation states that the polar moment of inertia for an area, with respect to an axis perpendicular to its plane, is equal to the sum of the moments of inertia about any two mutually perpendicular axes in its plane that intersect...  Applied Mechanics - Page 134de Charles Edward Fuller, William Atkinson Johnston - 1913Affichage du livre entier - À propos de ce livre
 | Samuel Earnshaw - 1844 - 462 pages
...The moment of inertia of any plane area with respect to a line through the origin perpendicular to its plane, is equal to the sum of the moments of inertia with respect to the axes of x and y. Let the figure be divided into an indefinitely large number of small masses, of... | |
 | George Pirie - 1875 - 236 pages
...co-ordinate (2) is always zero. Hence the moment of inertia of such a body about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two axes at right angles to one another in its plane. Hence we can infer that the moment of inertia... | |
 | Isaac Todhunter - 1878 - 442 pages
...is stated. 235. The moment of inertia of any plane figure about any straight line at right angles to its plane is equal to the sum of the moments of inertia about any two straight lines at right angles to each other in the plane which intersect at the first... | |
 | Edward Albert Bowser - 1884 - 550 pages
...intersection of the axes of x and y is 5 (& + f) dm. Hence the polar moment of inertia of any lamina is equal to the sum of the moments of inertia with respect to any tivo rectangular axes, lying in the plane of the lamina, COR. — For every two rectangular axes in... | |
 | Edward Albert Bowser - 1890 - 540 pages
...intersection of the axes of x and y is 2 (& + f) dm. Hence the polar moment of inertia of any lamina is equal to the sum of the moments of inertia with respect to any two rectangular axes, lying in the plane of the COB. — For every two rectangular axes in the plane of... | |
 | Mansfield Merriman - 1905 - 548 pages
...in (170) there results I\+l2=I* + Iv, that is, the sum of the principal moments of inertia is equal to the sum of the moments of inertia with respect to any two rectangular axes through the center of gravity. When /1 and /2 are known the moment of inertia /* with... | |
 | Stephen Elmer Slocum, Edward Lee Hancock - 1906 - 348 pages
...respect to its principal axes. Then Ip = 1^ + Iv and, consequently, C/ (22) + 1, = A + that is to say, the sum of the moments of inertia with respect to any two rectangular axes in the plane of the section is constant. (F) The numerical value of the moment of... | |
 | Oliver Clarence Lester - 1909 - 81 pages
...dxdy. Hence, adding equations XI, we obtain Theorem. The moment of inertia with respect to a point in a plane is equal to the sum of the moments of inertia with respect to two perpendicular axes lying in the plane and passing through the point. For a plane area equation... | |
 | William Duncan MacMillan - 1927 - 460 pages
...perpendicular planes which pass through that line. The moment of inertia with respect to any point is equal to the sum of the moments of inertia with respect to any three mutually perpendicular planes which pass through that point, or one-half the sum of the moments... | |
 | Research and Education Association - 1995 - 1098 pages
...parallel-axes theorem. Prove also that the moment of inertia of a thin plate about an axis at right angles to its plane is equal to the sum of the moments of inertia about two mutually perpendicular axes concurrent with the first and lying in the plane of the thin... | |
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