The Moments of Inertia

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Definition

Moment of inertia, denoted by the letter I, is another name for rotational inertia. It is associated with an object that is rotating about its center, or an axis. The moment of inertia for any rotating objects must be specified with respect to a chosen axis of rotation due to the varying distance r. The moment of inertia corresponds to mass for translational/linear motion.[1][2]


A Mathematical Model

The moment of inertia is the sum of mass times the square of perpendicular distance to the rotation axis, that is [math]\displaystyle{ I=\Sigma mr^2. }[/math]for all point mass components. This relationship is the basis for all other moments of inertia since any object can be built up from a collection of point masses.[3]

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