The second moment of area of any planar, closed shape is given by the following integral: Typical units for the moment of inertia, in metric, are: Typical units for the moment of inertia, in the imperial system of measurements are: By definition, the moment of inertia is the second moment of area, in other words the integral sum of cross-sectional area times the square distance from the axis of rotation, hence its dimensions are ^4. In fact, this is true for the moment of inertia of any shape, not just the circle.
Since those are lengths, one can expect that the units of moment of inertia should be of the type: ^4. The above equations for the moment of inertia of circle, reveal that the latter is analogous to the fourth power of circle radius or diameter. The moment of inertia of circle with respect to any axis passing through its centre, is given by the following expression:Įxpressed in terms of the circle diameter D, the above equation is equivalent to:
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