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An object is formed by attaching a uniform, thin rod with a mass of mr = 8kg and length L = 6 m to a uniform sphere with mass ms = 36.25 kg and radius R = 1.5m.1) What is the moment of inertia of the object about an axis at the left end of the rod?

An object is formed by attaching a uniform thin rod with a mass of mr 8kg and length L 6 m to a uniform sphere

Answer :

ANSWER:

2167.68 kg*m^2

STEP-BY-STEP EXPLANATION:

Given:

mr = 8 kg

L = 6 m

ms = 36.25 kg

R = 1.5 m

Moment of inertia of sphere about its center is:

[tex]I_{CM}=\frac{2}{5}m_s\cdot R^2[/tex]

Using paraller theorem, moment of inertia of shpere about end of rop is:

[tex]I_{\text{rod}}=m_s\cdot(R+L)^2+\frac{1}{3}m_r\cdot L^2[/tex]

Therefore:

[tex]\begin{gathered} I=I_{cm}+I_{\text{rod}}_{} \\ I=\frac{2}{5}\cdot m_s\cdot R^2+m_s\cdot(R+L)^2+\frac{1}{3}\cdot m_r\cdot L^2 \end{gathered}[/tex]

Replacing:

[tex]\begin{gathered} I=\frac{2}{5}\cdot36.25\cdot1.5^2+36.25\cdot(1.5+6)^2+\frac{1}{3}\cdot8\cdot6^2 \\ I=2167.69\text{ kg}\cdot m^2 \end{gathered}[/tex]

The moment of inertia is 2167.68 kg*m^2

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Rewritten by : Barada