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A hoop, a solid cylinder, a solid sphere, and a thin, spherical shell each have the same mass of 4.01 kg and the same radius of 0.260 m. (a) What is the moment of inertia (in kg · m2) for each object as it rotates about its axis

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Answer:

Given that

Radius ,r= 0.26 m

Mass ,m= 4.01 kg

Moment of inertia of hoop

I= m r²

[tex]I=4.01\times 0.26^2\ kg.m^2[/tex]

[tex]I=0.271\ kg.m^2[/tex]

Moment of inertia of solid cylinder

[tex]I=\dfrac{1}{2}mr^2[/tex]

[tex]I=\dfrac{1}{2}\times 4.01\times 0.26^2\ kg.m^2[/tex]

[tex]I=0.135\ kg.m^2[/tex]

Moment of inertia of solid sphere

[tex]I=\dfrac{2}{5}mr^2[/tex]

[tex]I=\dfrac{2}{5}\times 4.01\times 0.26^2\ kg.m^2[/tex]

[tex]I=0.108\ kg.m^2[/tex]

Moment of inertia of thin spherical

[tex]I=\dfrac{2}{3}mr^2[/tex]

[tex]I=\dfrac{2}{3}\times 4.01\times 0.26^2\ kg.m^2[/tex]

[tex]I=0.18\ kg.m^2[/tex]

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