Find the mass moment of inertia (I) of a rotating body for common shapes — solid cylinder, sphere, hoop, or rod — from its mass and radius or length. I measures how hard it is to change an object's spin.
Moment of inertia is the rotational analogue of mass: it measures an object's resistance to angular acceleration. It depends on both the total mass and how that mass is distributed relative to the rotation axis — mass farther from the axis contributes much more.
Each standard shape has a known formula, all of the form I = (coefficient)·M·R². Pick your shape, enter the mass and the radius (or length for a rod), and the calculator returns I in kg·m². Use it with τ = Iα or L = Iω for rotational dynamics.
It depends on shape. A solid cylinder/disc is I = ½MR², a solid sphere is I = 2/5 MR², a thin hoop is I = MR², and a rod about its centre is I = 1/12 ML².
Kilogram metres squared (kg·m²) in SI units — mass times distance squared.
Because all of a hoop's mass sits at the maximum radius, while a disc has mass spread inward. Inertia grows with the square of the distance from the axis, so the hoop's I is double the disc's.
It links torque to angular acceleration (τ = Iα) and defines rotational kinetic energy (½Iω²) and angular momentum (L = Iω), just as mass does for linear motion.