a C h y x b I x = bh 3 36 I x = bh 3 12 I y = bh (a 2 – ab + b 2 ) 36 I xy = bh 2 (2a – b) 72 I y = bh (a 2 + ab + b 2 ) 12 I xy = bh 2 (2a + b) 24 Triangle Half parabolic complement h x C y b I x = 37bh 3 2100 I x = bh 3 21 I y = b 3 h 80 I y = b 3 h 5 I xy = b 2 h 2 120 I xy = b 2 h 2 12 Half parabola h y x b C y = h ( x b ) 2 I x = 8bh 3 175 7 I y = 19b 3 h 15 I xy = b 2 h 2 6 I x = 2bh 3 I y = 2b 3 h I xy = b 2 h 2 480 60 Circular sector y R C x I x = R 4 (2 – sin2 ) 8 I y = R 4 (2 + sin2 ) 8 I xy =0 x = 4 3b y = 10 3h x = 8 3b y = 5 3h x = 3 2Rsin Quarter circle y x R C R I x = I y = 0.054 88 R 4 I xy = – 0.016 47 R 4 I x = I y = R 4 16 I xy = R 4 8 Quarter ellipse a y b C x x 2 + y 2 = 1 a 2 b 2 I x = 0.054 88ab 3 I x = ab 3 16 I y = 0.054 88a 3 b I y = a 3 b 16 I xy = – 0.016 47a 2 b 2 I xy = a 2 b 2 8 x = 3 4R y = 3 4R x = 3 4a y = 3 4b h b b 2 h 2 x y h b y x h 3 b 3 C C h x h 3 y b 2 b 2 C y x R C y x R 3π 4 Rectangle Circle I x = bh 3 12 I x = bh 3 3 I y = b 3 h 12 I y = b 3 h 3 I xy = 0 I xy = b 2 h 2 4 I x = I y = R 4 4 I xy = 0 Right triangle Semicircle I x = bh 3 36 I x = bh 3 12 I y = b 3 h 36 I y = b 3 h 12 I xy = – I xy = b 2 h 2 24 b 2 h 2 72 I x = 0.1098R 4 I xy = 0 I x = I y = R 4 8 π I xy = 0 Isosceles triangle I x = bh 3 36 I x = bh 3 12 I y = b 3 h 48 I xy = 0 I xy = 0 R C y = h 3 x = a+b 3 y = h ( x b ) 2 Area Moments of Inertia
