Why are centroid values different when computing using same equation

Hello,

I am trying to calculate a centroid of an annulus sector. First method is to st a range of radius and compute Centroid1. Second method, I use a loop to compute the Centroid2 using the same equation and plot the result in the graph. Why are the results different? Can someone please explain this?

Thanks in advance,

Sohail

%
clc
clear all
close all
%
Ro = [.5:.1:1.5]
Ri = Ro(1,1);
%
theta_r = 30; % 1/2 Angle in degrees
theta = theta_r * pi / 180; % converting angle to radians
%
Centroid1 = 2*Ro*sin(theta)/(3*theta)*(1-(Ro-Ri)/Ro+1/(2-(Ro-Ri)/Ro))
%
for i=1:11
    Centroid2(i) = 2*Ro(i)*sin(theta)/(3*theta)*(1-(Ro(i)-Ri)/Ro(i)+1/(2-(Ro(i)-Ri)/Ro(i)))
end
%
figure()
plot(Ro,Centroid1,'-ro', Ro,Centroid2,'-bo')
title('Why are Centroid Values Different Using Same Equation')
hleg1 = legend('Centroid_1','Centroid_2');
set(hleg1, 'Location', 'Northwest')
xlabel('Radius,(in)')
ylabel('rBar, (in)')

Answer 1

[Image Analyst]

You used matrix multiply "*" and matrix inverse ("/"), instead of element-by-element multiply and divide with dots ("./" and .*")

Corrected line of code:

Centroid1 = 2*Ro.*sin(theta)/(3*theta).*(1-(Ro-Ri)./Ro+1./(2-(Ro-Ri)./Ro))

Answer 2

[Matt J]

Because when computing Centroid1, you're using matrix multiplication and division instead of element-wise multiplication and division .* and ./

Answer 3

[Sohail]

Thanks Matt and Image Analyst for the explanation