What is Moment of Inertia?

The mass moment of inertia (also called rotational inertia) quantifies a body’s resistance to angular acceleration about a given axis. It is the rotational analog of mass in linear motion.

Where m is mass and r is the perpendicular distance from the axis of rotation.

Conversion Table

Unit	Symbol	= kg·m²
kilogram meter squared	kg·m²	1
kilogram centimeter squared	kg·cm²	1 × 10⁻⁴
gram centimeter squared	g·cm²	1 × 10⁻⁷
pound foot squared	lb·ft²	0.042140
pound inch squared	lb·in²	2.9264 × 10⁻⁴
ounce inch squared	oz·in²	1.8290 × 10⁻⁵
slug foot squared	slug·ft²	1.35582

Common Formulas for Simple Shapes

Shape	Axis	Formula
Solid cylinder/disk	Central axis	J = ½ m r²
Hollow cylinder	Central axis	J = ½ m (r₁² + r₂²)
Solid sphere	Through center	J = ⅖ m r²
Thin rod	Through center	J = ¹⁄₁₂ m L²
Thin rod	Through end	J = ⅓ m L²

Relationship to Torque and Angular Motion

Where τ is torque (N·m), J is moment of inertia (kg·m²), and α is angular acceleration (rad/s²).

Parallel Axis Theorem

The moment of inertia about any parallel axis equals the inertia about the center of mass plus m × d², where d is the distance between axes.