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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

Moments of Inertia Collections

Moments of Inertia Equations

  • Area MOI - Triangle I by vCalc
  • Area Moment of Inertia - Triangle (Rtdot Angle Right) by vCalc
  • MoI by vCalc
  • MoI - Annulus around diameter by vCalc
  • MoI - Box Around Center by vCalc
  • MoI - Box around edge by vCalc
  • MoI - circular cone around axis by vCalc
  • MoI - circular cone around vertex by vCalc
  • MoI - circular plate (center) by vCalc
  • MoI - circular plate (diameter) by vCalc
  • MoI - cylinder - axis by vCalc
  • MoI - cylinder - diameter at end by vCalc
  • MoI - cylinder - perpendicular to axis by vCalc
  • MoI - cylinder about x-axis by vCalc
  • MoI - cylinder about y-axis by vCalc
  • MoI - ellipsoid around a tangent parallel to one axis by vCalc
  • MoI - ellipsoid around one axis by vCalc
  • MoI - hollow cylinder (axis) by vCalc
  • MoI - hollow cylinder (diameter at end) by vCalc
  • MoI - hollow cylinder (perpendicular to axis) by vCalc
  • MoI - hollow sphere (2 radii) around diameter by vCalc
  • MoI - hollow sphere (2 radii) around tangent by vCalc
  • MoI - solid sphere around diameter by vCalc
  • MoI - solid sphere around tangent by vCalc
  • MoI - spherical shell around diameter by vCalc
  • MoI - spherical shell around tangent by vCalc
  • MoI - thin rectangular plate through center by vCalc
  • MoI - thin rectangular plate through center parallel to one side by vCalc
  • MoI - Thin Rod Through Center by vCalc
  • MoI - Thin Rod Through End by vCalc
  • MoI - torus around axis in the plane by vCalc
  • MoI - torus around axis perpendicular to plane by vCalc
  • MoI - Box around center by GerryPerham
  • MoI - thin rod through center by GerryPerham
  • MoI - thin rod through end by GerryPerham
  • Moment of Inertia (No External Torque) by Billy
  • Moment of Inertia - Cylindrical Shell by EmilyB
  • Moment of Inertia - Ellipsoid (`I_a`) by EmilyB
  • Moment of Inertia - Ellipsoid (`I_b`) by EmilyB
  • Moment of Inertia - Ellipsoid (`I_c`) by EmilyB
  • Moment of Inertia - Ellipsoid (axis_1 or axis_2) by MichaelBartmess
  • Moment of Inertia - Ellipsoid (axis_3) by MichaelBartmess
  • Moment of Inertia - Hollow Dodecahedron by EmilyB
  • Moment of Inertia - Hollow Icosahedron by EmilyB
  • Moment of Inertia - Hollow Octahedron by EmilyB
  • Moment of Inertia - Hollow Sphere by EmilyB
  • Moment of Inertia - Hollow Tetrahedron by EmilyB
  • Moment of Inertia - Hoop (`I_x, I_y`) by EmilyB
  • Moment of Inertia - Point Mass by EmilyB
  • Moment of Inertia - Rectangular Plate (axis center) by EmilyB
  • Moment of Inertia - Rectangular Plate (axis end) by EmilyB
  • Moment of Inertia - Right Circular Cone (`I_x, I_y`) by EmilyB
  • Moment of Inertia - Right Circular Cone (`I_z`) by EmilyB
  • Moment of Inertia - Rod rotating about center by EmilyB
  • Moment of Inertia - Rod rotating about end by EmilyB
  • Moment of Inertia - Solid Cuboid (`I_d`) by EmilyB
  • Moment of Inertia - Solid Cuboid (`I_h`) by EmilyB
  • Moment of Inertia - Solid Cuboid (`I_w`)