Polar Mass Moment of Inertia, Common Shape Equations and Calculator
Polar Mass Moment of Inertia About Axis A-A, Axis B-B and Axis C-C.
Mass Moments of Inertia, JM. 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 = 2πrdrρr2. 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; JM is used here to avoid confusion with moments of inertia of plane areas.
JM = Polar Mass Moment of Inertia (in-lbs-sec2, Kg-m-sec2)
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