Inertia formulas
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This document provides formulas for calculating the moment of inertia for common shapes about different axes. It gives the moment of inertia formulas for rectangles, triangles, circles, semi-circles, and ellipses. The formulas treat the moment of inertia about axes through the centroid (overbar notation) and parallel axes theorems which allow calculating the moment of inertia about any other axis given the distance from the centroidal axis.
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Inertia formulas
- 1. Useful Moment of Inertia Formulas Note: In the table below, the overbar indicates the moment of inertia is taken about an axis that passes through the centroid, denoted as ‘C’. Parallel axis theorems are: 2 AdII xx 2 AdII yy yxAII xyxy Here, A is the area of the shape, d is the distance from the centroidal axis to the desired parallel axis, and yx are the x and y distances of the centroid from the origin of the desired coordinate frame. Rectangle: 3 12 1 bhIx 3 3 1bhIx hbIy 3 12 1 hbIy 3 3 1 0yx I Area = bh Triangle: 3 36 1 bhIx 3 12 1 bhIx 72 )2( 2 hsbb Ixy bhArea 2 1 Circle: 4 4 1 rII yx 0yx I 2 rArea Semi-circle: 4 8 1 rII yx 4 ' 9 8 8 rIx 0yxI 2 2 r Area Ellipse: 3 4 1 abIx baIy 3 4 1 0yxI abArea Cr y x a b Cr y x 4r/3π x` Cr y x b h x x`C h/3 s y x y` x` b h C b/2 h/2