I = I_c + A d² shifts a moment of inertia to a parallel axis.
I = I_c + Ad² transfers the moment of inertia from the centroidal axis to a parallel axis at distance d. It lets you compute I for composite sections such as I-beams made of flanges and a web.
The flanges of an I-beam gain most of their I from the A d² term.
The parallel axis theorem is used constantly to compute the inertia of composite sections and rotating bodies about convenient axes.
I = I_c + A d² shifts a moment of inertia to a parallel axis.
The parallel axis theorem is used constantly to compute the inertia of composite sections and rotating bodies about convenient axes.
Only when the axis is parallel to the centroidal axis you already know. It does not apply to axes at an angle.
Moving an axis away from the centroid adds the area times the square of the distance, because every element is further away from the new axis.
Typical applications include finding the inertia of a T-section about its base, computing the moment of inertia of a flywheel about its shaft and checking the stiffness of a built-up girder from separate plates.
Study "Moment of inertia of area" first (topic 19 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Centroidal axis gives the minimum I. Sum parts about the common centroid. Same idea for mass moments.
The flanges of an I-beam gain most of their I from the A d² term.
The next topic is "Kinematics of a particle", which builds directly on this one.
It is classed as Beginner in Engineering Mechanics (topic 20 of 106). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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