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Finding the Curvature

  1. Nov 27, 2012 #1
    1. The problem statement, all variables and given/known data

    r(t)=<t^2,lnt,tlnt>

    2. Relevant equations

    k= |T '(t)| / |r '(t)|

    3. The attempt at a solution

    2llfsyu.jpg


    My professor's answer sheet solved the problem using the other method, k(t)=|r '(t) x r ''(t)| / |r '(t)|^3
    and that answer ends up being 0.3, while mine is 0.4. I can't see where I made any mistakes, and why I got 9 points marked off. Can someone explain?
     
  2. jcsd
  3. Nov 27, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    Yes. T(t) is supposed to be a unit vector for any value of t. You normalized it so that |T(1)|=1. But it's not a unit vector for any t. So your T'(t) comes out wrong.
     
  4. Nov 27, 2012 #3

    phyzguy

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    Science Advisor

    I think what you did wrong was when you calculated T(t), you plugged in |r'(1)| in the denominator, when you should have left it as |r'(t)| until after you differentiated T(t) to get T'(t). By doing this you lost the terms related to changes in |r'(t)|. Does this make sense?
     
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