Four small spheres, each of which you can regard as a point of mass m = 0.270 kg

Question

Four small spheres, each of which you can regard as a point of mass m = 0.270 kg, are arranged in a square d = 0.200 m on a side and connected by light rods (see figure below).

Four small spheres, each of which you can regard as a point of mass m = 0.150 kg, are arranged in a square d = 0.600 m on a side and connected by light rods (see figure below). 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). 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). 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.

Explanation / Answer

A)

I=4*m*r^2, where m=0.270 kg,

r= (0.200/2)*sqrt(2) is distance from O;

I = 4*0.27*[0.1414]^2

I= 1.08*0.01999

I=0.0216 kg*m^2;

B)

I = 4*m*r^2, where r=0.200/2;
I = 4*0.27*[0.200/2]^2

= 0.0108 kg/m^2;

C)

I = 2*m*r^2, where
r=((0.200/2)*sqrt(2)) is distance from diagonal;
I = 2*0.27*[0.1414]^2

= 0.010796 kg/m^2

=0.0108 kg/m^2

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