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Yahoo!

  • 3 years ago

Four rods of equal mass m each , Ab , BC , CA , DB are placed as shown. The moment of inertia of the system about B perpendicular to the plane ABC is (AB=a)

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  1. Yahoo!
    • 3 years ago
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    |dw:1360169550988:dw|

  2. Yahoo!
    • 3 years ago
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    @JamesJ

  3. JamesJ
    • 3 years ago
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    Obviously break down the problem rod by rod.

  4. JamesJ
    • 3 years ago
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    And if you're really stuck, you're just going to integrate rod by rod.

  5. Yahoo!
    • 3 years ago
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    I (BC) = ma^2/6 ryt ?

  6. shubhamsrg
    • 3 years ago
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    Its basically a maths ques, you just need to find rod lengths, after doing that you just have to calculate moment of inertia of each rod about B and add all

  7. Yahoo!
    • 3 years ago
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    Yup . i Have Calculated the length of rods BC = a/sqrt(2) , AC = a/sqrt(2) , DB = (sqrt2) * a / sqrt3

  8. Yahoo!
    • 3 years ago
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    I (BC) = ma^2/6 ryt ?

  9. shubhamsrg
    • 3 years ago
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    yep

  10. Yahoo!
    • 3 years ago
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    I (DB) = ma^2/18 ?

  11. shubhamsrg
    • 3 years ago
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    won' that be (2/9)ma^2

  12. Yahoo!
    • 3 years ago
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    Hw ?

  13. shubhamsrg
    • 3 years ago
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    |dw:1360246728479:dw|

  14. Yahoo!
    • 3 years ago
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    I (DB) = M L^2 / 3 * sin^2 30 ryt ?

  15. shubhamsrg
    • 3 years ago
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    why sin ?

  16. Yahoo!
    • 3 years ago
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    |dw:1360246891927:dw|

  17. shubhamsrg
    • 3 years ago
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    I don;t think angle matters

  18. shubhamsrg
    • 3 years ago
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    For calculation of I,

  19. shubhamsrg
    • 3 years ago
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    Because the axis is perpendicular to plane, the rod will make 90 degrees with the axis, doesn't matter how it is placed.

  20. shubhamsrg
    • 3 years ago
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    Do you have the final ans ?

  21. Yahoo!
    • 3 years ago
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    Yup 25 M a^2 / 18

  22. shubhamsrg
    • 3 years ago
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    <Lets see if we get that by my method>

  23. shubhamsrg
    • 3 years ago
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    So DB = 2M a^2 /9

  24. shubhamsrg
    • 3 years ago
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    And AC = ma^2/6 + 3ma^2/6 = 2ma^2 /3

  25. shubhamsrg
    • 3 years ago
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    So sum = ma^2 (2/3 + 2/9 + 1/6) = 19/18ma^2

  26. shubhamsrg
    • 3 years ago
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    hmm, okay doesn't match

  27. Yahoo!
    • 3 years ago
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    i think that angle matters

  28. shubhamsrg
    • 3 years ago
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    Wait I missed AB

  29. shubhamsrg
    • 3 years ago
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    AB = ma^2 /3 Sum = 25/18

  30. shubhamsrg
    • 3 years ago
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    Got it! B|

  31. Yahoo!
    • 3 years ago
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    But Hw Did u Claculate I (AC) ??

  32. shubhamsrg
    • 3 years ago
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    calculate about C, then B

  33. Yahoo!
    • 3 years ago
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    Ok...got it....:)

  34. shubhamsrg
    • 3 years ago
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    "Angle will not matter here" ;)

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