Four small spheres, each with a mass of m = 0.300 kg, are arranged in a square d

Question

Four small spheres, each with a mass of m = 0.300 kg, are arranged in a square d = 0.800 m on a side and connected by light rods.

(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).
kg·m2
(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).
kg·m2
(b) 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.
kg·m2

Explanation / Answer

1)

moment of inertial I = 4*m*r^2,

where m=0.3 kg,

r = (0.800/2)*sqrt(2) is distance from O;

I = 4*0.3*[(0.800/2)*sqrt(2)]^2 = 0.3839 kg*m^2

2) I = 4*m*r^2,

where r = 0.800/2

I = 4*0.3*[0.800/2]^2 = 0.192 kg/m^2

3)

I = 2*m*r^2,

where r = (0.800/2)*sqrt(2) is distance from diagonal;

I = 2*0.3*[(0.800/2)*sqrt(2)]^2= 0.1919 kg/m^2

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