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Moments of Inertia Collection

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Oct 18, 2019, 1:17:51 AM

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Oct 18, 2019, 1:17:51 AM

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Moments of Inertia

In physics and applied mathematics, the mass moment of inertia, usually denoted by $I$ $I$ , measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analogue to mass. Mass moments of inertia have units of dimension ML²([mass]*[length]²). It should not be confused with the second moment of area, which is used in bending calculations. The mass moment of inertia is often known as rotational inertia, and sometimes as the angular mass.
For simple objects with geometric symmetry, one can often determine the inertia in an exact closed-form expression. Typically this occurs when the mass density is constant, but in some cases the density can vary throughout the object as well. In general, it may not be straightforward to symbolically express the moment of inertia of shapes with more complicated mass distributions and lacking symmetry. When calculating moments of inertia, it is useful to remember that it is an additive function and exploit the parallel axis and perendicular axis therorms.

Description	Figure	Moment(s) of Inertia
Point Mass
Rod rotating about center
Rod rotating about end
Hoop
Solid Disk
Cylindrical Shell
Solid Cylinder
Thick-walled Cylinder		Using Density:
Tetrahedron
Octahedron
Dodecahedron
Icosahedron
Hollow Sphere
Solid Sphere
Sphere Shell
Right circular cone
Torus		About axis: About diameter:
Ellipsoid
Rectangular Plate rotating around end
Rectangular Plate rotating around center
Solid Cuboid

References

Wikipedia (https://en.wikipedia.org/wiki/List_of_moments_of_inertia)

Equations

Moment of Inertia - Point Mass EmilyB Use Equation
Moment of Inertia - Rod rotating about center EmilyB Use Equation
Moment of Inertia - Rod rotating about end EmilyB Use Equation
Moment of Inertia - Hoop ( $I_{z}$ $I_z$ ) EmilyB Use Equation
Moment of Inertia - Hoop ( $I_{x}, I_{y}$ $I_x, I_y$ ) EmilyB Use Equation
Moment of Inertia - Solid Disk ( $I_{z}$ $I_z$ ) EmilyB Use Equation
Moment of Inertia - Solid Disk ( $I_{x}, I_{y}$ $I_x, I_y$ ) EmilyB Use Equation
Moment of Inertia - Solid Cylinder ( $I_{z}$ $I_z$ ) EmilyB Use Equation
Moment of Inertia - Solid Cylinder ( $I_{x}, I_{y}$ $I_x, I_y$ ) EmilyB Use Equation
Moment of Inertia - Thick-walled Cylinder ( $I_{z}$ $I_z$ ) EmilyB Use Equation
Moment of Inertia - Thick-walled Cylinder ( $I_{x}, I_{y}$ $I_x, I_y$ ) EmilyB Use Equation
Moment of Inertia - Thick-walled Cylinder ( $I_{z}, ρ$ $I_z, rho$ ) EmilyB Use Equation
Moment of Inertia - Thick-walled Cylinder ( $I_{x}, I_{y}, ρ$ $I_x, I_y, rho$ ) EmilyB Use Equation
Moment of Inertia - Solid Tetrahedron EmilyB Use Equation
Moment of Inertia - Hollow Tetrahedron EmilyB Use Equation
Moment of Inertia - Solid Octahedron EmilyB Use Equation
Moment of Inertia - Hollow Octahedron EmilyB Use Equation
Moment of Inertia - Solid Dodecahedron EmilyB Use Equation
Moment of Inertia - Hollow Dodecahedron EmilyB Use Equation
Moment of Inertia - Solid Icosahedron EmilyB Use Equation
Moment of Inertia - Hollow Icosahedron EmilyB Use Equation
Moment of Inertia - Hollow Sphere EmilyB Use Equation
Moment of Inertia - Solid Sphere EmilyB Use Equation
Moment of Inertia - Sphere Shell EmilyB Use Equation
Moment of Inertia - Right Circular Cone ( $I_{z}$ $I_z$ ) EmilyB Use Equation
Moment of Inertia - Right Circular Cone ( $I_{x}, I_{y}$ $I_x, I_y$ ) EmilyB Use Equation
Moment of Inertia - Torus (about axis) EmilyB Use Equation
Moment of Inertia - Torus (about diameter) EmilyB Use Equation
Moment of Inertia - Ellipsoid ( $I_{a}$ $I_a$ ) EmilyB Use Equation
Moment of Inertia - Ellipsoid ( $I_{b}$ $I_b$ ) EmilyB Use Equation
Moment of Inertia - Ellipsoid ( $I_{c}$ $I_c$ ) EmilyB Use Equation
Moment of Inertia - Rectangular Plate (axis end) EmilyB Use Equation
Moment of Inertia - Rectangular Plate (axis center) EmilyB Use Equation
Moment of Inertia - Solid Cuboid ( $I_{h}$ $I_h$ ) EmilyB Use Equation
Moment of Inertia - Solid Cuboid ( $I_{w}$ $I_w$ ) EmilyB Use Equation
Moment of Inertia - Solid Cuboid ( $I_{d}$ $I_d$ ) EmilyB Use Equation
Moment of Inertia - Cylindrical Shell EmilyB Use Equation

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Spherical_shell_moment_of_inertia.png

Octahedral_axis.png

Moment_of_inertia_hollow_sphere.png

Recplaneoff.png

Moment_of_inertia_rod_end.png

Torus_cycles.png

Moment_of_inertia_disc.png

Moment_of_inertia_thin_cylinder.png

Moment_of_inertia_thick_cylinder_h.png

Moment_of_inertia_solid_cylinder.png

Moment_of_inertia_rod_center.svg.png

PointInertia.svg

Ellipsoid.png

Tetraaxial.png

Moment_of_inertia_solid_rectangular_prism.png

Recplane.png

Moment_of_inertia_cone.png

Moment_of_inertia_solid_sphere.png

Moment_of_inertia_hoop.png

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