Moment of Inertia of a Disk Calculator

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Moment of inertia measures how much an object resists changes to its rotational motion, playing the same role in rotational dynamics that mass plays in linear motion. For a uniform solid disk spinning about the axis through its center, perpendicular to its face, the moment of inertia is given by I = ½·m·r², where mass concentrated closer to the axis contributes less resistance to rotation than mass farther out — which is why a disk's moment of inertia is exactly half that of a ring or hoop with the same mass and radius.

This formula appears constantly in mechanical and automotive engineering — for flywheels, brake rotors, gears, and pulleys — as well as in introductory physics courses covering rotational kinetic energy and angular momentum. Engineers use it to size flywheels for energy storage, calculate the torque needed to spin up a rotating component, and predict how quickly a disk-shaped part will accelerate under a given applied torque.