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Geometrical Properties of Circular Sector


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Radius - r = m

Angle - α = °

k = π/180

a = r2·(1 – cos(α)) m

Area

A = α/2·k·r2 m2

Centroid

yc = a/2 m

zc = 4·r·sin(α/2)/(3·α·k) m

Perimeter

P = (α·k + 2)·r m

Second moments of area

Iy = r4·((α·k + sin(α))/8 – 8·sin(α/2)2/(9·α·k)) m4

Iz = r4·(α·ksin(α))/8 m4

Polar moment of area

Ix = Iy + Iz m4

Radii of gyration

ry = √Iy/A m

rz = √Iz/A m

rx = √Ix/A m


Substitute