Question

3. (25) Determine the moment of inertia of the shaded area about the y-axis. A=ar2 3 in 3 in 1x = {art 6 in. Circular area A = {bh Triangular area

Answer 1

3inch 3inch binch --- Zringle-to-* Tuinch Solution Calculating moment of inerties of treengle about " [I ] I,= Ia, + A sea of Triangle [ Distence] => Parabel Axis theorem » Is= bna + 4x6x3* [3*}] Here b= 6inch H=3inch I = 148.5 inch 4 > I,= 6x33 +44 - 36 Calculating moment of about Y. (Iz) Inutia of Bottom Rectengle FC ED

Iz = Igaz + Asea of Recteuple [bestuce] Is = 446 +24[3] Iz = 280 inchy [13] Calculating Morment of Irreeta of Top Rectangle about Y Is = Iazt Area [Distence] ² > Is= 6*2° +18 [115] Iz = su inchy Now calculating moment of Intention of urcle about [Iy] Iy = I can + Aseax [Dis tence]" Iy = 2(3)" + PSP [3]" = [2]"+R[2]*[9] Iy= 125-66 inchu

Hence Total moment of Inestia about Y [I] I = I + Iz t Iz - In I = 148.5 + 288 + 54–12566 I=364.8 inchy to Ansee