Mass Moment of Inertia
Calculate the Moment of Inertia for various geometric shapes and mass distributions. Moment of Inertia measures an object's resistance to change in rotation direction.
| Shape | Formula | Parameters | Moment of Inertia (kg m²) |
|---|---|---|---|
| Point Mass | I = m r² | m (kg), r (m) | =inputs.mass_point * inputs.distance_point ^ 2 |
| Thin-walled Hollow Cylinder | I = m r² | m (kg), r (m) | =inputs.mass_cylinder * inputs.radius_cylinder ^ 2 |
| Hollow Cylinder | I = 1/2 m (ri² + ro²) | m (kg), ri (m), ro (m) | =0.5 * inputs.mass_hollow_cyl * (inputs.radius_inner ^ 2 + inputs.radius_outer ^ 2) |
| Solid Cylinder | I = 1/2 m r² | m (kg), r (m) | =0.5 * inputs.mass_solid_cyl * inputs.radius_solid_cyl ^ 2 |
| Circular Disk | I = 1/2 m r² | m (kg), r (m) | =0.5 * inputs.mass_disk * inputs.radius_disk ^ 2 |
| Thin-walled Hollow Sphere | I = 2/3 m r² | m (kg), r (m) | =0.667 * inputs.mass_sphere_hollow * inputs.radius_sphere_hollow ^ 2 |
| Solid Sphere | I = 2/5 m r² | m (kg), r (m) | =0.4 * inputs.mass_sphere_solid * inputs.radius_sphere_solid ^ 2 |
| Rectangular Plane (center axis) | I = 1/12 m (a² + b²) | m (kg), a (m), b (m) | =inputs.mass_rect / 12 * (inputs.side_a ^ 2 + inputs.side_b ^ 2) |
| Rectangular Plane (edge axis) | I = 1/3 m a² | m (kg), a (m) | =inputs.mass_rect_edge / 3 * inputs.side_a_edge ^ 2 |
| Slender Rod (center axis) | I = 1/12 m L² | m (kg), L (m) | =inputs.mass_rod / 12 * inputs.length_rod ^ 2 |
| Slender Rod (end axis) | I = 1/3 m L² | m (kg), L (m) | =inputs.mass_rod_end / 3 * inputs.length_rod_end ^ 2 |
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Moment of Inertia-- kg m²
Calculator
Inputs
Results
Moment of Inertia-- kg m²
Calculator
Inputs
Results
Moment of Inertia-- kg m²
Calculator
Inputs
Results
Moment of Inertia-- kg m²
Calculator
Inputs
Results
Moment of Inertia-- kg m²
Calculator
Inputs
Results
Moment of Inertia-- kg m²