An object is formed by attaching a uniform, thin rod with a mass of mr = 6.85 kg and length L = 5.76 m to a uniform sphere with mass ms

Question

An object is formed by attaching a uniform, thin rod with a mass of mr = 6.85 kg and length L = 5.76 m to a uniform sphere with mass ms = 34.25 kg and radius R = 1.44 m. Note ms = 5mr and L = 4R.
What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)

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Ngọc Diệp 5 hours 2021-07-22T04:49:17+00:00 1 Answers 0 views 0

Answers ( )

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    2021-07-22T04:50:47+00:00

    Answer:

    153.9 kgm^2

    Explanation:

    We are given that

    m_r=6.85 kg

    Length,L=5.76 m

    m_s=34.25 kg

    Radius,R=1.44 m

    We have to find the moment of inertia of the object about an axis at the center of mass of the object.

    Moment of inertia of the object about an axis at the center of mass of the object,I=I_r+I_s=\frac{1}{12}m_rL^2+m_r(\frac{L}{2}+\frac{R}{2})^2+\frac{13}{20}m_sR^2

    Substitute the values

    I=\frac{1}{12}(6.85)(5.76)^2+6.85(\frac{5.76}{2}+\frac{1.44}{2})^2+\frac{13}{20}(34.25)(1.44)^2

    I=153.9 kgm^2

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