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The moment of inertia of a thin uniform ...

The moment of inertia of a thin uniform rod about an axis passing through its centre and perpendicular to its length is `I_(0)`. What is the moment of inertia of the rod about an axis passing through one end and perpendicular to the rod ?

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The moment of inertia (MI) of a thin uniform rod, of mass M and length L, about a transverse axis through its centre of mass is
`I_(CM)=(ML_(2))/(12)" "`.....(i)
Let I be its MI about a transverse axis through its end. By the theorem of parallel axis, `I=I_(CM)+Mh^(2)" "`.......(2)
In this case, h=distance between the parallel axes`=(L)/(2)`.

`:. I=(ML^(2))/(12)+M((L)/(2))^(2)=(ML^(2))/(12)+(ML^(2))/(4)`
`=(ML^(2))/(12)(1+3)=(ML^(2))/(3)" "`.....(3)
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Knowledge Check

  • The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I_(0) . Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

    A
    `I_(0) +ML^(2)//2`
    B
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    C
    `I_(0) + 2ML^(2)`
    D
    `I_(0) + ML^(2)`

  • The moment of inertia of a copper disc, rotating about an axis passing through its centre and perpendicular to its plane

    A
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    B
    changes if its axis of rotation is changed
    C
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    D
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  • The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its mid-point and perpendicular to its length is I_0 . Its moment of inertia about an axis passing through one of its ends perpendicular to its length is.

    A
    `I_0 + ML^2//4`
    B
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    C
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