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Theorem of parallel axes

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(a) Prove the theorem of perpendicular axes. (Hint : Square of the distance of a point (x, y) in the x-y plane from an axis through the origin and perpendicular to the plane is ^(x2)+y^(2)) . (b) Prove the theorem of parallel axes. (Hint : If the centre of mass of a system of n particles is chosen to be the origin summ_(i)r_(i)=0 ).

State and prove the theorem of parallel axis about moment of inertia.

Knowledge Check

  • If a body is lying in the Y-Z plane, then according to theorem of perpendiculr axes the correct expression will be

    A
    `I_(z)=I_(x)+I_(y)`
    B
    `I_(y)=I_(x)+I_(z)`
    C
    `I_(x)=I_(y)+I_(z)`
    D
    `I_(y)=I_(z)+Md^(2)`

  • The theorem of perpendicular axes is applicable for

    A
    only planar bodies
    B
    only regular shaped bodies
    C
    only three dimensional bodies
    D
    None of the above

  • The parallel axis theorem can be applied to

    A
    any two parallel axes
    B
    any two parallel-axes of which one must lie within the body
    C
    any two parallel-axes of which one must pass through the centre of mass of the body.
    D
    any two parallel axes lying in the plane of the body

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    Find the equations of the lines parallel to axes and passing through (-2,3).

    Find the equation of the lines parallel to axes and passing through (-3,4).

    The two lines of regression are parallel to the axes if r = ……………..

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