Geometrical Properties of Quarter Circle

Radius - r =   m

Area

A = π·r²4 m²

Centroid

z_c = y_c = 4·r3·π m

Perimeter

P = (π2 + 2)·r m

Second moments of area

I_z = I_y = (π16 – 49·π)·r⁴ m⁴

I_yz = (18 – 49·π)·r⁴ m⁴

Principal area moments

I₁ = I_y + abs(I_yz) m⁴

I₂ = I_y – abs(I_yz) m⁴

Angle of principal axis

α₁ = atan(I_y – I₁I_yz) ^о

Polar moment of area

I_x = 2·I_y m⁴

Radii of gyration

r_z = r_y =  I_yA m

r₁ =  I₁A m

r₂ =  I₂A m

r_x =  I_xA m