...Radii of Gyration about Parallel Axes. 193. The moment of inertia of a body about any axis exceeds its moment of inertia about a parallel axis passing through the centre of gravity, by the product of the mass and the square of the distance between the axes. Let h be the distance between...

...to the middle ordinate, and having obtained this, the necessary modification in order to determine the moment of inertia about a parallel axis passing through the centre of gravity of the water section is readily obtained by deducting from the result the area of the water-plane multiplied...

...theorem is very simple and may be left to the reader, ie the moment of inertia about any axis is equal to the moment of inertia about a parallel axis passing through the centre of gravity, together with the product of the mass and the square of the distance between the axes. 1 ml3 ml3 _=_...

...where A is the whole area of surface. It is thus seen that (a) The moment of inertia of a plane area about any axis is equal to the sum of the moment of inertia about a parallel axis through the centre of gravity of the area and the product of the area by the square of the distance...

...article often facilitate the calculation of moments of inertia. Theorem I. — The moment of inertia C' about any axis is equal to the sum of the moment of inertia C about a parallel axis through the center of mass and the product of the mass m of the body by the...

...article often facilitate the calculation of moments of inertia. Theorem I. — The moment of inertia C' about any axis is equal to the sum of the moment of inertia C about a parallel axis through the center of mass and the product of the mass m of the body by the...

...the axis of rotation passes through its centre of gravity because the moment of inertia, I of a body about any axis is equal to the sum of the moment of inertia lg about a parallel axis passing through its centre of gravity and the product of its mass M to the...

...X2 A 3.2.3 or I = Ic + ;c2 A 3.2.4 Similarly Ix = IG + y1 A 3.2.5 The moment of inertia of an area about any axis is equal to the sum of the moment of inertia about a parallel axis through the centroid and the product of the area and the square of the distance between this axis and...

...Hence /0 = / g + M x Thus, the theorem of parallel axes states that the moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through the centre of gravity and the product of the mass...