 Show that the moment of inertia of a body about any axis is equal to the moment of inertia about a parallel axis through the center of mass plus the product of the mass of the body and the square of the distance between the axes.  The Calculus for Engineers - Page 81by John Perry - 1897 - 378 pagesFull view - About this book
 | William Nathaniel Griffin - Dynamics, Rigid - 1847 - 130 pages
...the following properties. 5. To connect the moment of inertia of a rigid body about any axis with its moment of inertia about a parallel axis through the centre of gravity. Let P be a particle whose mass is m (fig. 1), A, G the traces of two straight lines on a plane through... | |
 | Mathematics - 1868 - 276 pages
...plane. It is also known* that the moment of inertia about any axis whatever, is equal to the moment about a parallel axis through the centre of gravity, together with the moment which the whole mass, if collected at the centre of gravity, would have about the original axis.... | |
 | Mathematics - 1868 - 272 pages
...plane. It is also known* that the moment of inertia about any axis whatever, is equal to the moment about a parallel axis through the centre of gravity, together with the moment which the whole mass, if collected at the centre of gravity, would have about the original axis.... | |
 | William Thomson Baron Kelvin, Peter Guthrie Tait - Mechanics, Analytic - 1872 - 316 pages
...; and the second proposition above is equivalent to — The moment of inertia of a system about any axis is equal to the moment of inertia about a parallel axis through the centre of inertia, /, together with the moment of inertia, about the first axis, of the whole mass supposed condensed... | |
 | Richard Wormell - Dynamics - 1876 - 282 pages
...velocity. 132. Proposition XXX.— The moment of inertia of a system of heavy particles about a given axis is equal to the moment of inertia about a parallel...axis through the centre of gravity, together with the product of the whole mass by the square of the distance of the centre of gravity from the given axis.... | |
 | Samuel James Pope Thearle - Naval architecture - 1877 - 384 pages
...of the system about these two axes. 4. The moment of inertia of a body or system of bodies about any axis is equal to the moment of inertia about a parallel axis, through the centre of gravity, plus the moment of inertia of the whole mass collected at the centre of gravity about the original... | |
 | Isaac Todhunter - 1878 - 144 pages
...notation of Art. 259. The moment of inertia about the edge of length c is -5- (a2 + 52). By Art. 233 the moment of inertia about a parallel axis through the centre of gravity will be - (a2 + 62) - J/p2, where p o is the distance between the two axes. Nowp2=^-j — ; so that... | |
 | Edward John Routh - Dynamics, Rigid - 1882 - 408 pages
...products about all other parallel axes. The moment of inertia of a body or system of bodies about any axis is equal to the moment of inertia about a parallel axis through the centre of gravity plus the moment of inertia of the whole mass collected at the centre of gravity about the original... | |
 | William Steadman Aldis - Dynamics, Rigid - 1882 - 156 pages
...= 0 by the properties of the centre of inertia. That is, the moment of inertia about the axis of z is equal to the moment of inertia about a parallel axis through the centre of inertia added to the product of the whole mass into the square of the distance between the two axes.... | |
 | William Kingdon Clifford - Mathematics - 1882 - 358 pages
...Vol. iv. pp. 78—81.] ON THE PRINCIPAL AXES OF A RIGID BODY. 35 axis whatever, is equal to the moment about a parallel axis through the centre of gravity, together with the moment which the whole mass, if collected at the centre of gravity, would have about the original axis.... | |
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