Moments of Inertia
The moment of inertia, aka the angular mass or rotational inertia, of a rigid body determines the torque needed for a desired angular acceleration about a rotational axis. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation.
It is an extensive (additive) property: the moment of inertia of a composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis).
vCalc's Moments of Inertia folder contains equations pertaining to the angular mass.
Parent Categories
Moments of Inertia Calculators and Collections
Moments of Inertia Equations
- Area MOI - Triangle I KurtHeckman Use Equation
- Area Moment of Inertia - Triangle (Rt. Angle Right) MichaelBartmess Use Equation
- Cylinder MoI about Central Axis GerryPerham Use Equation
- Cylinder MoI about the End GerryPerham Use Equation
- Cylinder MoI Perpendicular to Axis GerryPerham Use Equation
- MoI MichaelBartmess Use Equation
- MoI - Annulus around diameter GerryPerham Use Equation
- MoI - Box Around Center MichaelBartmess Use Equation
- MoI - Box around center GerryPerham Use Equation
- MoI - Box around edge GerryPerham Use Equation
- MoI - circular cone around axis GerryPerham Use Equation
- MoI - circular cone around vertex GerryPerham Use Equation
- MoI - circular plate (center) GerryPerham Use Equation
- MoI - circular plate (diameter) GerryPerham Use Equation
- MoI - cylinder about x-axis MichaelBartmess Use Equation
- MoI - cylinder about y-axis MichaelBartmess Use Equation
- MoI - ellipsoid around a tangent parallel to one axis GerryPerham Use Equation
- MoI - ellipsoid around one axis GerryPerham Use Equation
- MoI - hollow cylinder (axis) GerryPerham Use Equation
- MoI - hollow cylinder (diameter at end) GerryPerham Use Equation
- MoI - hollow cylinder (perpendicular to axis) GerryPerham Use Equation
- MoI - hollow sphere (2 radii) around diameter GerryPerham Use Equation
- MoI - hollow sphere (2 radii) around tangent GerryPerham Use Equation
- MoI - solid sphere around diameter GerryPerham Use Equation
- MoI - solid sphere around tangent GerryPerham Use Equation
- MoI - spherical shell around diameter GerryPerham Use Equation
- MoI - spherical shell around tangent GerryPerham Use Equation
- MoI - thin rectangular plate through center GerryPerham Use Equation
- MoI - thin rectangular plate through center parallel to one side GerryPerham Use Equation
- MoI - Thin Rod Through Center MichaelBartmess Use Equation
- MoI - thin rod through center GerryPerham Use Equation
- MoI - Thin Rod Through End MichaelBartmess Use Equation
- MoI - thin rod through end GerryPerham Use Equation
- MoI - torus around axis in the plane GerryPerham Use Equation
- MoI - torus around axis perpendicular to plane GerryPerham Use Equation
- Moment of Inertia (No External Torque) Billy Use Equation
- Moment of Inertia - Cylindrical Shell EmilyB Use Equation
- Moment of Inertia - Ellipsoid (axis_1 or axis_2) MichaelBartmess Use Equation
- Moment of Inertia - Ellipsoid (axis_3) MichaelBartmess Use Equation
- Moment of Inertia - Ellipsoid (Ia) EmilyB Use Equation
- Moment of Inertia - Ellipsoid (Ib) EmilyB Use Equation
- Moment of Inertia - Ellipsoid (Ic) EmilyB Use Equation
- Moment of Inertia - Hollow Dodecahedron EmilyB Use Equation
- Moment of Inertia - Hollow Icosahedron EmilyB Use Equation
- Moment of Inertia - Hollow Octahedron EmilyB Use Equation
- Moment of Inertia - Hollow Sphere EmilyB Use Equation
- Moment of Inertia - Hollow Tetrahedron EmilyB Use Equation
- Moment of Inertia - Hoop (Ix,Iy) EmilyB Use Equation
- Moment of Inertia - Point Mass EmilyB Use Equation
- Moment of Inertia - Rectangular Plate (axis center) EmilyB Use Equation
- Moment of Inertia - Rectangular Plate (axis end) EmilyB Use Equation
- Moment of Inertia - Right Circular Cone (Ix,Iy) EmilyB Use Equation
- Moment of Inertia - Right Circular Cone (Iz) 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 - Solid Cuboid (Id) EmilyB Use Equation
- Moment of Inertia - Solid Cuboid (Ih) EmilyB Use Equation
- Moment of Inertia - Solid Cuboid (Iw) EmilyB Use Equation
- Moment of Inertia - Solid Cylinder (Ix,Iy) EmilyB Use Equation
- Moment of Inertia - Solid Cylinder (Iz) EmilyB Use Equation
- Moment of Inertia - Solid Disk (Ix,Iy) EmilyB Use Equation
- Moment of Inertia - Solid Disk (Iz) EmilyB Use Equation
- Moment of Inertia - Solid Dodecahedron EmilyB Use Equation
- Moment of Inertia - Solid Icosahedron EmilyB Use Equation
- Moment of Inertia - Solid Octahedron EmilyB Use Equation
- Moment of Inertia - Solid Sphere EmilyB Use Equation
- Moment of Inertia - Solid Tetrahedron EmilyB Use Equation
- Moment of Inertia - Sphere Shell EmilyB Use Equation
- Moment of Inertia - Thick-walled Cylinder (Ix,Iy,ρ) EmilyB Use Equation
- Moment of Inertia - Thick-walled Cylinder (Ix,Iy) EmilyB Use Equation
- Moment of Inertia - Thick-walled Cylinder (Iz,ρ) EmilyB Use Equation
- Moment of Inertia - Thick-walled Cylinder (Iz) EmilyB Use Equation
- Moment of Inertia - Torus (about axis) EmilyB Use Equation
- Moment of Inertia - Torus (about diameter) EmilyB Use Equation
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