Four small spheres, each of which you can regard as a point of mass m = 0.120 kg

Question

Four small spheres, each of which you can regard as a point of mass m = 0.120 kg, are arranged in a square d = 0.550 m on a side and connected by light rods (see figure below).

(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

(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.
kg · m2

Explanation / Answer

distance of the center from the corners r = sqrt((d/2)^2 + (d/2)^2

r = sqrt((0.55/2)^2+(0.55/2)^2) = 0.388 m

part(a)

moment of inertial = I = 4*m*r^2 = 0.0726 kg m^2

part(b)

the perpendicular distance of the masses from AB = r = d/2 =
0.55/2 = 0.275 m

the moment of inertia =I = 4*m*r^2 = 4*0.12*0.275^2 = 0.0363 kg m^2

part(c)

here tha axes is the diagonal

the perpendicular distance of the masses on the axes = 0

the perepndicular distance of the upper right and lower left is = r = 0.388 m

moment of inertia = I = 2*m*r^2 = 0.0363 kg m^2

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