The principle directions determine the best way to orient a beam to for maximum stiffness, and how much asymmetrical beams, like channels and angles, will twist when a load is applied. When the coordinate axes are oriented in the principle directions, the centroidal moments of inertia are maximum about one axis and minimum about the other, but neither is necessarily zero. Mass Moment of Inertia (Moment of Inertia) - I - is a measure of an objects resistance to change in rotation direction. If the product of inertia is not zero it is always possible to rotate the coordinate system until it is, in which case the new coordinate axes are called the principle axes. The product of inertia will be zero for symmetrical objects when a coordinate axis is also an axis of symmetry. , where F is the force creating the moment, and r is a position vector from the moment center to the line of action of the force. ![]() Unlike the rectangular moments of inertia, which are always positive, the product of inertia may be either positive, negative, or zero, depending on the object's shape and the orientation of the coordinate axes. It is an extensive (additive) property: for a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of.
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