Question

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?

Answer 1

2167.68 kg*m^2

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:

`I_(CM)=(2)/(5)m_s\cdot R^2`

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

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

Therefore:

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

Replacing:

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

The moment of inertia is 2167.68 kg*m^2