Area Moment of Inertia
The parallel axes rule also applies to the second moment of area (area moment of inertia) for a plane region D:
where:
- is the area moment of inertia of D relative to the parallel axis;
- is the area moment of inertia of D relative to its centroid;
- is the area of the plane region D;
- is the distance from the new axis z to the centroid of the plane region D.
Note: The centroid of D coincides with the centre of gravity (CG) of a physical plate with the same shape that has uniform density.
THEOREM The moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass times the square of the distance between the two parallel axes.Read more about this topic: Parallel Axes Rule
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