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List of moments of inertia
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List of moments of inertia

The following is a list of moments of inertia.

Table of contents
1 Area moments of inertia
2 Mass moments of inertia

Area moments of inertia

Area moments of inertia have units of dimension length4. Each is with respect to a horizontal axis through the centroid of the given shape, unless otherwise specified.

Circles and related areas

For a filled circular area of radius , .

For a filled semicircle with radius resting atop the -axis, .

For a filled quarter circle with radius entirely in the upper-right quadrant of the Cartesian plane, .

For an ellipse whose radius along the -axis is and whose radius along the -axis is , .

Rectangle

For a filled rectangular area with a base width of and height , .

For an axis collinear with the base, . (This is a trivial result from the parallel axis theorem.)

Triangle

For a filled triangular area with a base width of and height , .

For an axis collinear with the base, . (This is a consequence of the parallel axis theorem and the fact that the distance between these two axes is always .)

Mass moments of inertia

Mass moments of inertia have units of dimension mass × length2.

Description Figure Moment(s) of inertia Comment
Thin cylindrical shell with open ends, of radius and mass
Thick cylinder with open ends, of inner radius , outer radius and mass
Solid cylinder of radius , height and mass
Thin disk of radius and mass
Solid sphere of radius and mass
Hollow sphere of radius and mass
Right circular cone with radius , and mass
Solid rectangular prism of height , width , and depth , and mass

For a similarly oriented cube with sides of length and mass , .
Rod of length and mass This expression is an approximation, and assumes that the mass of the rod is distributed in the form of an infinitely thin (but rigid) wire.
Rod of length and mass This expression is an approximation, and assumes that the mass of the rod is distributed in the form of an infinitely thin (but rigid) wire.