An Elementary Treatise On Rigid Dynamics

Cover An Elementary Treatise On Rigid Dynamics
An Elementary Treatise On Rigid Dynamics
W J William James Loudon
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+ q%my i + —mpq.
. '. S mxy = Imx'y' + M • pq.
Proposition II. — In the case of a lamina, the moment of inertia about any axis perpendicular to its plane is equal to the sum of the moments about any tivo perpendicular lines drawn in the plane through the point where the axis meets the lamina.
For /= 1m(x 2 +y 2 ) = -7nx 2 + -my 2 .
Proposition III. — To find the moment of inertia of a body about any line, knowing the moment and products of inertia about any three rectangular axes drawn through
...some point on this line.
In Fig. 7 let the three rectangular axes be OX, OY, OZ, and let P be any point of the body (x, y, z) } and ON any line drawn from O, inclined at angles «, j3, 7 to the axes.
Then /about ON=1mPN 2, PN being perpendicular to OX, and PX 2 = OP 2 - 0X 2 = (. V 2 +/+;-) - (. R cos« + j

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