Four small 0.500 kg spheres, each of which you can regard as a point mass, are a

Question

Four small 0.500 kg spheres, each of which you can regard as a point mass, are arranged in a square 0.400 m on a side and connected by light rods. (See (Figure 1) .)

Part A

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

Express your answer in kilogram meters squared to three significant figures.

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Part B

Find the moment of inertia of the system about an axis along the line AB.

Express your answer in kilogram meters squared to three significant figures.

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Part C

Find the moment of inertia of the system about an axis along the line CD.

Express your answer in kilogram meters squared to three significant figures.

Four small 0.500 kg spheres, each of which you can regard as a point mass, are arranged in a square 0.400 m on a side and connected by light rods. (See (Figure 1) .)

Part A

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

Express your answer in kilogram meters squared to three significant figures.

kgm2

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Part B

Find the moment of inertia of the system about an axis along the line AB.

Express your answer in kilogram meters squared to three significant figures.

kgm2

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Part C

Find the moment of inertia of the system about an axis along the line CD.

Express your answer in kilogram meters squared to three significant figures.

kgm2   

Explanation / Answer

a)

the moment of inertia of the system about an axis (a) through the center of square is

I=4mR2

Here R=sqrt[(0.4/2)2+(0.4/2)2]=0.2828 m

I=4*0.5*0.28282=0.16 Kg-m2

b)

the moment of inertia of the system about an axis along the line AB.

I=4mR2=4*0.5*(0.4/2)2=0.08 Kg-m2

c)

the moment of inertia of the system about an axis along the line CD

I=2mR2=2*0.5*(0.2828)2

I=0.2828 Kg-m2

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