Moment of Inertia

Moment of Inertia, a mechanical quantity that plays in rotational motion the same role that mass plays in translational motion. For example, acceleration in translational motion is inversely proportional to mass, while acceleration of rotational motion (angular acceleration) is inversely proportional to the moment of inertia; the kinetic energy of translational motion equals ¹/₂mv², while that of rotational motion equals ¹/₂Iw², where I is the moment of inertia and w is the angular velocity. The moment of inertia is numerically equal to the sum of the products of the masses of the points of a body by the squares of the distances of these masses from the axis of rotation: I = Σmr², where Σ is the summation sign. The summation is generally performed by means of integral calculus. For geometrically simple bodies, calculations give simple expressions for the moment of inertia. Thus, the moment of inertia of a sphere relative to an axis passing through its center equals ²/₅M R², where M is the mass of the sphere and R is its radius; the moment of inertia of a circular disk relative to an axis passing through its center and perpendicular to the plane of the disk equals ¹/₂M R², and so on.