Moment of Inertia Converter
Convert between various units of moment of inertia (e.g., kg·m², lb·ft², g·cm²).
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Understanding Moment of Inertia
Moment of Inertia (I), also known as mass moment of inertia or rotational inertia, is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similarly to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments indicating more resistance to change in rotational speed.
The SI unit for moment of inertia is kilogram meter squared (kg·m²).
Common Moment of Inertia Formulas (for uniform density)
| Shape | Axis of Rotation | Formula |
|---|---|---|
| Point Mass (m) at distance (r) | Through point, perpendicular to r | I = mr² |
| Thin Rod (length L, mass m) | Center, perpendicular to length | I = (1/12)mL² |
| Thin Rod (length L, mass m) | End, perpendicular to length | I = (1/3)mL² |
| Solid Cylinder (radius R, mass m) | Central axis | I = (1/2)mR² |
| Hollow Cylinder (inner R1, outer R2, mass m) | Central axis | I = (1/2)m(R₁² + R₂²) |
| Solid Sphere (radius R, mass m) | Any axis through center | I = (2/5)mR² |
| Thin Spherical Shell (radius R, mass m) | Any axis through center | I = (2/3)mR² |