Question

Determine the coordinates of the centroid of the plane area shown in Fig. with reference to the axis shown. Take x = 40 mm.

Answer 1

The composite figure is divided into the following simple figures: (1) A rectangle 

A₁ = (14x) × (12x) = 168x² 

x₁ = 7x; y₁ = 6x

(3) A rectangle to be subtracted 

A₃ = (–4x) × (4x) = –16x² 

x₃ = 2x; y₃ = 8x + 2x = 10x 

(4) A semicircle to be subtracted

(5) A quarter of a circle to be subtracted

Total area A = 168x² + 12x² – 16x² – 8πx² – 4πx² 

= 126.3009x²

ΣA_iy_i = 168x² × 6x + 12x² × \(\frac{4x}3\) - 16x² × 10x – 8πx² × \(\frac{16x}{3\pi}\) – 4πx² × 10.3023x

Centroid is at (326.40, 219.12).