University study material for Meccanica dei Fluidi con Fondamenti di Ingegneria Chimica in the Chemical Engineering degree programme at Politecnico di Milano. The document covers: 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,
University study material for Meccanica dei Fluidi con Fondamenti di Ingegneria Chimica in the Chemical Engineering degree programme at Politecnico di Milano. The document covers: 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,
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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 bhI x 3 3 1bhI x hbI y 3 12 1 hbI y 3 3 1 0yxI Area = bh Triangle: 3 36 1 bhI x 3 12 1 bhI x 72 )2( 2hsbbI xy bhArea 2 1 Circle: 4 4 1 rII yx 0yxI 2rArea Semi-circle: 4 8 1 rII yx 4 ' 9 8 8 rI x 0yxI 2 2rArea Ellipse: 3 4 1 abI x baI y 3 4 1 0yxI abArea y x y` x` b h C b/2 h/2 b h x x` C h/3 s C r y x C r y x 4r/3π x` C r y x a b
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