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Find curvature of spiral of archimedes

  1. Jul 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the curvature of the spiral of Archimedes r = 2θ

    2. Relevant equations

    ||v x a || / ||v||^3


    3. The attempt at a solution

    I tried to convert the polar equation into parametric and got
    x = 2θsinθ
    y = 2θsinθ
    z = 0

    I think took the derivative of x y and z and got

    x' = -2θsinθ + 2cosθ
    y' = 2θcosθ + 2sinθ
    z' = 0

    I then put them into vectors and used the cross product to get v x a and got the magnitude to be 4θ^2. I found ||v||^3 to be 8θ^3 so I got || v x a || / ||v^3|| = (1/2θ) .
     
  2. jcsd
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