What is Moment of Inertia?

The moment of inertia (I) is a measure of an object’s resistance to changes in its rotation rate. It depends on the mass distribution relative to the axis of rotation.

Formula

For discrete masses: I = Σmᵢrᵢ²
For continuous masses: I = ∫r²dm

Common Formulas

• Rectangle (centroid): I = (1/12) × m × (w² + h²)
• Circle (centroid): I = (1/2) × m × r²
• Solid sphere: I = (2/5) × m × r²
• Hollow cylinder: I = m × r²