physics

Three identical thin rods, each of length L and mass m, are welded perpendicular to one another as shown below. The assembly is rotated about an axis that passes through the end of one rod and is parallel to another. Determine the moment of inertia of this structure. (Answer in terms of m and L.)
- for my answer i go t 2Ma^2 but this is not right?

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  1. I cant make out the figure.

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    bobpursley
  2. for the simplicity let us assume that the rods are thin with the radius much less than L, junction of
    the rods as the origin of the coordinates and the axis of rotation as the z axis
    for the rod along the y axis we get
    I = (1 / 3) m L2
    for the rod parallel to the z axis the parallel axis theorem gives
    I = (1 / 2) m r2 + m (L / 2)2
    = (1 / 4) m L2
    in the rod we can see that along the x axis the bit of the material between x and x+ dx has a mass
    (m / L) dx
    and is at a distance
    r = √[x2 + (L / 2)2] from the axis of rotation
    so the total rotational inertia will be
    Itotal = (1 / 3) m L2 + (1 / 4) m L2 + -L/2∫L/2 [x2 + (L2 / 4)] (m / L) dx
    =
    I will let you do the calculation.

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  3. (11/12)mL^2

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