The Moment of Inertia of a circular area of diameter 'd' about its diameter axis is-

Explanation

Concept: Parallel Axis Theorem: The moment of inertia of a body about an axisparallel to the body passing through its center is equal to the sumofmomentofinertia of the body about the axis passing through the center and product of the area of the bodytimes the square of the distance between the two axes I = I com + Ax2 Calculation: dϕ = ​dx + ∂x ∂ϕ ​dy = ∂y ∂ϕ 0 ​ = dx dy − ​ = ​ ∂y ∂ϕ ​ ∂x ∂ϕ − ​v u = ​ ​ = ( dx dy) 1 − ​v u ​ ​ = ( dx dy) 2 ​u v ​ ​ × ( dx dy) 1 ​ ​ = ( dx dy) 2 − ​ × v u ​ = u v −1 Given: The Moment of Inertia of a circle about the centroidal axis is: Important Points The following table shows the Second moment of inertia of different shapes I ​ = xx I ​ = yy ​ ⇒ 64 πd4 ​ 4 πr4 Shape Figure Moment of Inertia Rectangle Triangle Circle Semicircle Quarter circle I ​ = xx ​ 12 bd3 I ​ = yy ​ 12 db3 I ​ = xx ​ 36 bh3 I ​ = yy ​ 36 hb3 I ​ = xx ​d 64 π 4 I ​ = yy ​d 64 π 4 I ​ = xx 0.11R4 I ​ = yy ​R 8 π 4 I ​ = xx 0.055R4