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Finding the moment of inertia

  1. Apr 1, 2013 #1
    1. The problem statement, all variables and given/known data

    Two uniform square laminas are combined into a single body. One lamina ABCD has mass 5m and the other lamina PQRS has mass m. The lamina PQRS has side 2a, and its vertices are at the mid-points of the sides of ABCD, with P on AB and S on AD. The line PS meets AC at K, and the body rotates in a vertical plane about a horizontal axis k through K (see diagram). Find the moment of inertia of the body about k.

    2. Relevant equations

    parallel and the perpendicular axes theorems

    3. The attempt at a solution

    If i understand the question correctly, is the "dashed"(broken)line, the axis about which we need to find the moment of inertia ? If that is the case, here is what i did :


    Using the perpendicular axes theorem : (let [itex]I_{A}[/itex] be the moment of inertia about the required axis for ABCD only)
    2[itex]I_{A}[/itex] = [itex]\frac{5m(2a^{2}+2a^{2})}{3}[/itex]
    [itex]I_{A}[/itex] = [itex]\frac{10ma^{2}}{3}[/itex]

    Similarly, let [itex]I_{B}[/itex] be the moment of inertia about the required axis for PQRS only :
    Using the perpendicular axes theorem,
    [itex]I_{B}[/itex] = [itex]\frac{ma^{2}}{3}[/itex]

    The total moment of inertia = [itex]I_{A}[/itex] + [itex]I_{B}[/itex]
    Total = [itex]\frac{11ma^{2}}{3}[/itex]

    The problem is that the solution notes state the answer to be [itex]\frac{40ma^{2}}{3}[/itex]
     

    Attached Files:

  2. jcsd
  3. Apr 1, 2013 #2

    rude man

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    Since k was not indicated on the diagram it's a bit of a puzzle all right as to what the axis of rotation is. It's supposed to be a "horizontal" axis which would seem to eliminate the dashed line though. I think the intended axis is a "hozizontal" line passing thru point K. In other words, the axis of rotation is parallel to line AB, and also to a line drawn thru SQ, and situated inbetween those two and passing thru point K.

    Happy integration!
     
  4. Apr 1, 2013 #3

    haruspex

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    I would interpret rotating "in a ... plane" as meaning the axis is perpendicular to the lamina.
     
  5. Apr 2, 2013 #4

    rude man

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    That sounds sound. I agree.
     
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