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Homework Help: Find the curvature?

  1. Jan 17, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the curvature of r(t)=2ti+2tj+k.

    2. Relevant equations

    3. The attempt at a solution
    The answer is 0 in the book.
    I know the formula for curvature is k(t)=abs(r'(t)xr"(t))/abs(r'(t))^3. I know that r'(t)=2i+2j and r"(t)=0, so r'(t)xr"(t)=0? How to find r'(t)xr"(t) and r'(t)^3?
  2. jcsd
  3. Jan 17, 2015 #2


    Staff: Mentor

    r'(t)r''(t) = 0, which you already found. What is |r'(t)|? Note that this means the magnitude or length of r'(t).
  4. Jan 18, 2015 #3
    So how do I find abs(r'(t))? That's where I got stuck.
  5. Jan 18, 2015 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    The notation |r'(t)| does not mean the absolute value of r'(t), it means to find the magnitude of the vector r'(t). Think Pythagoras.
  6. Jan 18, 2015 #5


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The problem is that Math10 quoted the formula using abs() instead of modulus.
    It should be ##k(t)=\frac{|\dot{\vec r}(t)\times \ddot {\vec r}(t)|}{|\dot{\vec r}(t)|^3}##
  7. Jan 18, 2015 #6


    Staff: Mentor

    Three of us have told you that |r'(t)| does not mean "absolute value". It means "magnitude" or "length" of the vector r'(t).
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