Polar Mass Moment of Inertia About Axis A-A and B-B of Common Shapes

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Polar Mass Moment of Inertia About Axis A-A, Axis B-B and Axis C-C.

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.

Polar Mass Moment of Inertia of a Hollow Circular Section

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.

2nd moment of the strip

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-sec²)
h, b, l, L = Distance (in, m)
M = Mass = ρL = (lb - sec² / in, N - Sec² / m )
ρ = Density

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Section	Mass Polar Moment of Inertia Axis A-A J_M	Mass Polar Moment of Inertia Axis B-B J_M
Mass Polar Moment of Inertia Prism ^Open Polar Mass Moment of Inertia Prism Calculator
Mass Polar Moment of Inertia Cylinder ^Open Polar Mass Moment of Inertia Cylinder Calculator
Mass Polar Moment of Inertia Hollow Cylinder ^Open Polar Mass Moment of Inertia Hollow Cylinder Calculator
Mass Polar Moment of Inertia Pyramid, Rectangular Base ^Open Polar Mass Moment of Inertia Pyramid, Rectangular Base Calculator		Through the center of gravity
Mass Polar Moment of Inertia Sphere ^Open Polar Mass Moment of Inertia Sphere Calculator
Mass Polar Moment of Inertia Spherical Sector ^Open Polar Mass Moment of Inertia Spherical Sector Calculator		-
Mass Polar Moment of Inertia Spherical Segment ^Open Polar Mass Moment of Inertia Spherical Segment Calculator		-
Mass Polar Moment of Inertia Torus ^Open Polar Mass Moment of Inertia Torus Calculator
Mass Polar Moment of Inertia Paraboloid ^Open Polar Mass Moment of Inertia Parabolid Calculator		Through the center of gravity
Mass Polar Moment of Inertia Cone ^Open Polar Mass Moment of Inertia Cone Calculator		Through the center of gravity
Mass Polar Moment of Inertia Frustum of Cone ^Open Polar Mass Moment of Inertia Frustum of Cone Calculator		-

Section	Mass Polar Moment of Inertia Axis A-A J_M	Mass Polar Moment of Inertia Axis B-B J_M	Mass Polar Moment of Inertia Axis C-C J_M
Mass Polar Moment of Inertia Ellipsoid ^Open Polar Mass Moment of Inertia Ellipsoid Calculator

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