Aim-calculate the principle moment of intertia 0f a ring(2D) by evaluating the moment of inertia tensor,further show that- Also,plot the corresponds of a ring in 2D space and principle moment

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Apparatus- 

Scilab software, Laptop .

Algorithm- 

1. Give the value of number of points .

2. Give the value of radius of the ring and mass of the ring .

4. Using the ‘for loop’ on the equation of mass .

5. write the identity matrix (3,3), repreoentating ‘d’ in inertia tensor .

6. Using the ‘linspace’ command for show the maximum value between 0 to n .

7. write the polar equation .

8. show the value of x1,y1,z1 represent all x,y,z coordinates respectably .

9. Give the equation of ‘r2’ which represent r2=(x1.*x1)+(y1.*y1)+(z1.*z1 ) .

10. Again using the 2 ‘for loop’ representing index ‘ab’ of I(a,b) .

11. write the equation of inertia tensor matrix .

12. Display the inertia tensor matrix .

13. Using the ‘spec’ command for find the eigen value of principle axis .

14. Display the value of first,second and third principle axis .

15. Using the for loop and plot the graph .

16. Plot the graph in the four coordinates .

17. Using the ‘xgrid’ command .

18. label the graph by using the label command .

INPUT-

n=100

r=1//in cm

M=1//in gm

for i=1:n

m(i)=M/n

end

d=eye(3,3)

c=linspace(0,2*%pi,n)

X=r*cos(c)

Y=r*sin(c)

for i=1:n

x(i,1)=X(i)

x(i,2)=Y(i)

x(i,3)=0

end

x1=x(:,1)

y1=x(:,2)

z1=x(:,3)

r2=(x1.*x1)+(y1.*y1)+(z1.*z1)

for a=1:3

for b=1:3

I(a,b)=0

for i=1:n

I(a,b)=I(a,b)+(m(i)*(d(a,b)*r2(i)-x(i,a)*x(i,b)))

end

end

end

disp(I,'moment of inertia')

[pa,mpa]=spec(I)

disp(pa(:,1),'first principal value')

disp(pa(:,2),'second principal value')

disp(pa(:,3),'third principal value')

for s=1:n

plot(X(s),Y(s),'+')

end

disp(I)

xa=[-pa(1,1), pa(1,1)]

yb=[-pa(2,1), pa(2,1)]

plot(xa,yb)

xa=[-pa(1,2), pa(1,2)]

yb=[-pa(2,2), pa(2,2)]

plot(xa,yb)

xgrid

xlabel("X-AXIS")

ylabel("Y-AXIS")

OUTPUT-

moment of inertia

0.495 0. 0.

0. 0.505 0.

0. 0. 1.

first principal value

1.

0.

0.

second principal value

0.

1.

0.

third principal value

0.

0.

1.