...through its centre of gravity ; and z(r^m) expresses its moment of inertia with respect to the axis KK' parallel to the first axis, and at a distance from...second member of equation [b] may be put under the form or, denoting 2(Y 2 ,») = M(k* + a 2 .) ................ [c] 46. The determination of the moments of...

...through its centre of gravity ; and 2(r2?«) expresses its moment of inertia with respect to the axis KK' parallel to the first axis, and at a distance from...the mass of the body by the square of the 'distance Ictween the two axes. The second member of equation [b] may be put under the form or, denoting !&!»)...

...in relation to an axis parallel to the first, and passing through the centre of gravity of the body, plus the product of the mass of the body, by the square of the distance of the two axes. 188. Principle of vis viva in the motion of rotation about an axis.— It follows,...

...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 tJte distance of the two axes from each other. We see from this that of all the moments of inertia...

...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...

...parallel axis passing through the centre of gravity, increased by the product of the entire weight of the body by the square of the distance between the two axes. PROOF. — Refer the body to a system of three rectangular axes, OX, OY, and OZ, of which OZ is the...

...equal to its moment of inertia with respect to a parallel line through the centre of mass, increased by the product of the mass of the body by the square of the perpendicular distance from the centre of mass to the given line. The least principal moment of inertia...

...axis is equal to the moment of inertia with reference to a parallel axis through the centre of mass, plus the product of the mass of the body by the square of the distance between the two axes. This is called the theorem of moment of inertia for parallel axes. By means of it we can find /' for...

...line is equal to the moment of inertia with reference to a parallel line through the centre of mass, plus the product of the mass of the body by the square of the distance between the two lines. If therefore we know I and d, we can find /', or conversely, if we know I ' and d, we can find...

...is equal to the moment of inertia about a parallel axis through the center of gravity increased by the product of the mass of the body by the square of the distance between the parallel axes. Let G be the center of gravity of the body and A the position of the parallel axis....