Moment of Inertia: 4 Spheres Connected by Rods in Square

[amm617]

Homework Statement

Four small spheres, each of which you can regard as a point of mass 0.200 , are arranged in a square 0.400 on a side and connected by light rods.

The picture has 4 spheres connected by rods in the shape of a square. there's a point O in the middle of the square and a horizontal line through the point O with point A on one end and point B on the other end.

a)Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane (an axis through point O in the figure).

b)Find the moment of inertia of the system about an axis bisecting two opposite sides of the square (an axis along the line AB in the figure).

c)Find the moment of inertia of the system about an axis that passes through the centers of the upper left and lower right spheres and through point O.


I=m1(r1^2)+m2(r2^2)+...

 

[member 553083]

Homework Equations I=m1(r1^2)+m2(r2^2)+...The Attempt at a Solution a)I=m1(r1^2)+m2(r2^2)+m3(r3^2)+m4(r4^2)I=(0.200)(0.2^2)+(0.200)(0.2^2)+(0.200)(0.2^2)+(0.200)(0.2^2)=0.0032 kgm^2b)I=(0.200)(0.2^2)+(0.200)(0.2^2)+(0.200)(0.2^2)+(0.200)(0.2^2)+(0.200)(0.4^2)=0.0192 kgm^2c)I=(0.200)(0.2^2)+(0.200)(0.2^2)+(0.200)(0.4^2)=0.0128 kgm^2