Moment of Inertia Calculator Formula

Understand the math behind the moment of inertia calculator. Each variable explained with a worked example.

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Formulas Used

Moment of Inertia

inertia = (shape == 1) ? (2/5) * mass * pow(radius, 2) : ((shape == 2) ? (2/3) * mass * pow(radius, 2) : ((shape == 3) ? 0.5 * mass * pow(radius, 2) : (1/12) * mass * pow(2 * radius, 2)))

Variables

VariableDescriptionDefault
shapeShape1
massMass(kg)5
radiusRadius (or half-length for rod)(m)0.2

How It Works

Moment of Inertia

Moment of inertia (I) is the rotational analogue of mass. It depends on mass distribution relative to the rotation axis.

Formulas by Shape

  • Solid Sphere: I = (2/5) * m * r²
  • Hollow Sphere: I = (2/3) * m * r²
  • Solid Cylinder/Disk: I = (1/2) * m * r²
  • Thin Rod (center): I = (1/12) * m * L²

    • Worked Example

    A solid sphere of mass 5 kg and radius 0.2 m.

    shape = 1mass = 5radius = 0.2
    1. 01For a solid sphere: I = (2/5) * m * r²
    2. 02I = 0.4 * 5 * 0.04
    3. 03I = 0.4 * 0.2
    4. 04I = 0.08 kg·m²

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