Why Does a Ring Have a Higher Moment of Inertia Than a Solid Disc of Equal Mass and Outer Radius?

Northwestern University explains that a ring has a higher moment of inertia than a solid disk of equal mass and outer radius because it has less mass at its center. According to the principles of inertia, bodies that have more mass at the center have lower levels of moment of inertia, which is directly related to the rate at which an object can spin.

If a wooden disk and a metal ring of equal radius and equal mass are rotated down an inclined plane, each will register a distinct acceleration. If both objects are given an equal push, the metal ring will spin longer than the disk, because it has a greater moment of inertia. Nevertheless, if the two objects are rolled from the same point and at the same time on an inclined plane, the wooden disk’s lesser moment of inertia will cause it to reach the bottom first.

Knowledge of moments of inertia of planets has made it possible to understand their distribution of mass. An understanding of these principles is also critical in the design of satellites. Altering distribution of mass affects the location of the spin axis, which in turn changes the moment of inertia.