Polar Mass Moment of Inertia, Common Shape Equations and Calculator
Engineering Metals and Materials Table of Contents Polar Mass Moment of Inertia About Axis A-A, Axis B-B and Axis C-C. Related: Polar Area Moment of Inertia and Section Modulus. Mass Moments of Inertia, J_{M}. formulas for mass moment of inertia of various solids are given below. Example, Polar Mass Moment of Inertia of a Hollow Circular Section: A strip of width dr on a hollow circular section, whose inner radius is r and outer radius is R. The mass of the strip = 2πrdrρ, where ρ is the density of material. In order to get the mass of an individual section, integrate the mass of the strip from r to R.
The 2nd moment of the strip about the AA axis = 2πrdrρr^{2}. To find the polar moment of inertia about the AA axis, integrate the 2nd moment from r to R.
Note: In some many engineering examples the symbol I denotes the polar moment of inertia of masses; J_{M} is used here to avoid confusion with moments of inertia of plane areas. Where: J_{M} = Polar Mass Moment of Inertia (in-lbs-sec^{2, }Kg-m-sec^{2})
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