A measure of an object's resistance to changes in its rotational motion. Depends on the mass distribution relative to the axis of rotation. Key parameter in angular acceleration and torque calculations.
| Shape | Formula | Axis |
|---|---|---|
| Solid Cylinder | I = ½MR² | Central axis |
| Hollow Cylinder | I = MR² | Central axis |
| Solid Sphere | I = ⅖MR² | Through center |
| Thin Rod | I = ¹⁄₁₂ML² | Through center |
A geometric property of a cross-section that measures its resistance to bending and deflection. Also known as the second moment of area. Critical for beam design and structural analysis.
| Shape | Formula | Axis |
|---|---|---|
| Rectangle | I = bh³/12 | Centroidal axis |
| Circle | I = πr⁴/4 | Through center |
| Hollow Circle | I = π(r₀⁴ - rᵢ⁴)/4 | Through center |
| I-Beam | I = (BH³ - bh³)/12 | Major axis |
A measure of an object's resistance to torsion or twisting. For circular shafts, it's the sum of the area moments of inertia about two perpendicular axes in the cross-section.
| Shape | Formula | Axis |
|---|---|---|
| Solid Circle | J = πd⁴/32 | Central axis |
| Hollow Circle | J = π(d₀⁴ - dᵢ⁴)/32 | Central axis |
| Rectangle | J = bh(b² + h²)/12 | Centroidal axis |