Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by light rods. Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane.

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Question:

Four small spheres, each of which you can regard as a point of mass 0.200 kg, are arranged in a square 0.400 m on a side and connected by light rods. Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane.

Answer:

The moment of inertia of the system about an axis through the center of the square, perpendicular to its plane is .

Given data:

The mass of each sphere is, .

Length of side of square is, .

The expression for the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane is,

Here,

R is the distance between center of the square and the sphere. And its value is,

Then, moment of inertia is,

Thus, the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane is .

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