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anonymous

  • 4 years ago

How do I know when to use M=u*(r X F) or M= r X F to find the Momentum

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  1. anonymous
    • 4 years ago
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    Is that u times (r cross F) or is X a variable?\[M = u \cdot (r \times F) ~~ {\rm or}~~ M = u \cdot (r \cdot X \cdot F)\]

  2. anonymous
    • 4 years ago
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    times

  3. anonymous
    • 4 years ago
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    r cross F

  4. anonymous
    • 4 years ago
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    u dot product ( r cross product F)

  5. anonymous
    • 4 years ago
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    Okay. Another question: What quantity is u? I want to make sure we are on the same page here. I have a feeling we are defining angular momentum here and not translation momentum.

  6. anonymous
    • 4 years ago
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  7. anonymous
    • 4 years ago
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    u needs to be found

  8. anonymous
    • 4 years ago
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    I know how to do it because the book shows it using the cartesian values but my question is when a problem is given to find M , how do I know if I use M=u*(r X F) or just M = r X F

  9. anonymous
    • 4 years ago
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    I got it. You are looking to calculate the moment not momentum. I would always use\[M = r \times F\]I don't know what u represents. If I know what it is, I can advise you on how to use it.

  10. anonymous
    • 4 years ago
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    In the example you have given, to find the moment about point A, using the following expression. \[M_A = [0.6 \hat i + 0.3 \hat k] \times [-300 \hat k] = (0.6 \cdot -300) \cdot [\hat i \times \hat k] + (0.3 \cdot -300) \cdot [\hat k \times \hat k] = (0.6 \cdot 300) \hat j\]

  11. anonymous
    • 4 years ago
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    \[M_A = (0.6 \cdot 300) \hat j\]

  12. anonymous
    • 4 years ago
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    u is the vector AB

  13. anonymous
    • 4 years ago
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    beccause the problem says find the Mab produced by the Force

  14. anonymous
    • 4 years ago
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    To find the moment about point B, \[M_B = [0.2 \hat i - 0.2 \hat j + 0.3 \hat k] \times -300 \hat k\]

  15. anonymous
    • 4 years ago
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    For a moment about the line through A and B, \[M_{AB} = \vec u_{A/B} \cdot (\vec r_o \times F_C)\]where \(\vec r_o\) is the vector from any point of the segment AB to C.

  16. anonymous
    • 4 years ago
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    We use the vector \(\vec u_{A/B}\) when we are finding the moment about a line or axis. We use the regular cross product when we are finding the moment about a point.

  17. anonymous
    • 4 years ago
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    \[M_{line} = \vec u \cdot (r_o \times F)\]\[M_{point} = r \times F\]

  18. anonymous
    • 4 years ago
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    Perfect!!!!! Thank you soooooo much!!! Couldn't be explained better!!!!

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