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The moment of inertia of a body with the shape of the cross-section is the second moment of this area about the -axis perpendicular to the cross-section, weighted by its density. This is also called the polar moment of the area, and is the sum of the second moments about the - and -axes. [24]
The second polar moment of area, also known (incorrectly, colloquially) as "polar moment of inertia" or even "moment of inertia", is a quantity used to describe resistance to torsional deformation (), in objects (or segments of an object) with an invariant cross-section and no significant warping or out-of-plane deformation. [1]
The moments of inertia of a mass have units of dimension ML 2 ([mass] × [length] 2). It should not be confused with the second moment of area, which has units of dimension L 4 ([length] 4) and is used in beam calculations. The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass.
The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The unit of dimension of the second moment of area is length to fourth power, L 4, and should not be confused with the mass moment of inertia.
In planetary sciences, the moment of inertia factor or normalized polar moment of inertia is a dimensionless quantity that characterizes the radial distribution of mass inside a planet or satellite. Since a moment of inertia has dimensions of mass times length squared, the moment of inertia factor is the coefficient that multiplies these.
ν E = 1.19 is the normalized Euler frequency (in units of reciprocal years), C = 8.04 × 10 37 kg m 2 is the polar moment of inertia of the Earth, A is its mean equatorial moment of inertia, and C − A = 2.61 × 10 35 kg m 2. [2] [7] The observed angle between the figure axis of the Earth F and its angular momentum M is a few hundred ...
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Bending moment, a moment that results in the bending of a structural element; First moment of area, a property of an object related to its resistance to shear stress; Second moment of area, a property of an object related to its resistance to bending and deflection; Polar moment of inertia, a property of an object related to its resistance to ...