Mass moment of inertia

Engineering Fundamentals


The mass moment of inertia measures the extent to which an object resists rotational acceleration about a particular axis, and is the rotational analogue to mass. The torque needed to achieve an angular acceleration is defined by:


The mass moment of inertia for several shapes is shown in the table below.

FigureDescriptionMass moment of inertia
Mass moment of inertia casePoint mass$$I=mr^2$$
Mass moment of inertia caseRod of length l and mass mWith l>>r
Mass moment of inertia caseSolid cylinder$$I=\frac{1}{2}mr^2$$
Mass moment of inertia caseCylindrical shellWith r>>t
Mass moment of inertia caseSphere$$I=\frac{2}{5}mr^2$$

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