Centroid & moi table
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This document provides formulas for calculating various geometric properties of common shapes including: 1) Length, centroid location, and moment of inertia for circular arcs, straight lines, rectangles, triangles, semicircles, quadrants and full circles. 2) Area formulas for rectangles, triangles, semicircles, quadrants and full circles. 3) Centroid locations and moments of inertia about the centroid for rectangles, triangles, semicircles, quadrants and full circles.
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Centroid & moi table
- 1. Figure Length & Centroid Area & Centroid Area Momentof Inertia Circulararc 𝐿 = 2𝛼𝑟 𝑥 𝑐 = 𝑟𝑠𝑖𝑛𝛼 𝛼 𝑦𝑐 = 0 Quartercircular arc 𝐿 = 𝜋𝑟 2 𝑥 𝑐 = 2𝑟 𝜋 𝑦𝑐 = 2𝑟 𝜋 Semicirculararc 𝐿 = 𝜋𝑟 𝑥 𝑐 = 𝑟 𝑦𝑐 = 2𝑟 𝜋 Straightline 𝐿 = √ 𝑎2 + 𝑏2 𝑥 𝑐 = 𝑎 2⁄ 𝑦𝑐 = 𝑏 2⁄ RectangularArea 𝐴 = 𝑏ℎ 𝑥 𝑐 = 𝑏 2⁄ 𝑦𝑐 = ℎ 2⁄ 𝐼 𝑥 = 𝑏ℎ3 3⁄ 𝐼 𝑦 = ℎ𝑏3 3⁄ 𝐼 𝑥 𝑐 = 𝑏ℎ3 12⁄ 𝐼 𝑦𝑐 = ℎ𝑏3 12⁄
- 2. TriangularArea 𝐴 = 𝑏ℎ 2 𝑥 𝑐 = 2𝑏 3⁄ 𝑦𝑐 = ℎ 3⁄ 𝐼 𝑥 = 𝑏ℎ3 12⁄ 𝐼 𝑦 = ℎ𝑏3 4⁄ 𝐼 𝑥 𝑐 = 𝑏ℎ3 36⁄ 𝐼 𝑦𝑐 = ℎ𝑏3 36⁄ TriangularArea 𝐴 = 𝑏ℎ 2 𝑥 𝑐 = 𝑏 3⁄ 𝑦𝑐 = ℎ 3⁄ 𝐼 𝑥 = 𝑏ℎ3 12⁄ 𝐼 𝑦 = ℎ𝑏3 12⁄ 𝐼 𝑥 𝑐 = 𝑏ℎ3 36⁄ 𝐼 𝑦𝑐 = ℎ𝑏3 36⁄ Triangulararea 𝐴 = 𝑏ℎ 2 𝑥 𝑐 = 𝑏 2⁄ 𝑦𝑐 = ℎ 3⁄ 𝐼 𝑥 = 𝑏ℎ3 12⁄ 𝐼 𝑦 = 7𝑏3ℎ 48⁄ 𝐼 𝑥 𝑐 = 𝑏ℎ3 36⁄ 𝐼 𝑦𝑐 = ℎ𝑏3 48⁄ Quadrantarea of a circle 𝐴 = 𝜋𝑟2 4 𝑥 𝑐 = 4𝑟 3𝜋⁄ 𝑦𝑐 = 4𝑟 3𝜋⁄ 𝐼 𝑥 = 𝜋𝑟4 16⁄ 𝐼 𝑦 = 𝜋𝑟4 16⁄ 𝐼 𝑥 𝑐 = ( 𝜋 16 − 4 9𝜋 ) 𝑟4 𝐼 𝑦𝑐 = ( 𝜋 16 − 4 9𝜋 ) 𝑟4 Semicirculararea 𝐴 = 𝜋𝑟2 2 𝑥 𝑐 = 𝑟 𝑦𝑐 = 4𝑟 3𝜋⁄ 𝐼 𝑥 = 𝜋𝑟4 8⁄ 𝐼 𝑦 = 5𝜋𝑟4 8⁄ 𝐼 𝑥 𝑐 = ( 𝜋 8 − 8 9𝜋 ) 𝑟4 𝐼 𝑦𝑐 = 𝜋𝑟4 8⁄ Circulararea 𝐴 = 𝜋𝑟2 𝑥 𝑐 = 𝑟 𝑦𝑐 = 𝑟 𝐼 𝑥 = 5𝜋𝑟4 4⁄ 𝐼 𝑦 = 5𝜋𝑟4 4⁄ 𝐼 𝑥 𝑐 = 𝜋𝑟4 4⁄ 𝐼 𝑦𝑐 = 𝜋𝑟4 4⁄