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Note that for a sphere, Rm = Rf, and am = Of,. For a cylinder, Rm=°° and the hoop stress is twice the meridional stress.

Mass moment of inertia (MOI) is a measure of a solid's tendency to resist rotational forces. Rotational inertia depends on mass distribution and varies with the axis of revolution selected as a reference. The MOI for a solid will always be smallest for an axis passing through its center of mass* (Fig. 11-39).

"For an arbitrary mass with an orthogonal coordinate system (x, y, z) located at its center of mass, the moment of inertia about, say, the x-axis is

M01a = imbme(yZ + Z2)pdV = /„^(y2 +z2)dm where y and z are the distances from the x axis in the y and z directions to the elemental volume, dV, and p is the density of the material. Using the parallel axis theorem, the MOI about an axis parallel to x is

MOIxV = MOIja + <ly2 + lz2)m where ly and lz are the distances from the x to x' axis in the y and z directions.

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