1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Curvature problem

  1. Jul 7, 2012 #1
    1. The problem statement, all variables and given/known data
    Given the polar function r = 4cos(3θ) find the curvature.

    2. Relevant equations

    3. The attempt at a solution

    I know there is a formula for curvature of a polar function but I was never given that equation and was told to convert to parametric. and use ||v x a|| / ||v||^3. So this is my work
    Converting to parametric:

    x = 4cos(3θ)cos(θ)
    y= 4cos(3θ)sin(θ)
    z = 0

    to get v i took the derivative

    x' = -12sin(3θ)cos(θ) - 4cos(3θ)sin(θ)
    y' = -12sin(3θ)sin(θ) + 4 cos(4θ)cos(θ)
    z' = 0

    I then took the second derivative to get a

    x'' = -40cos(3θ)cos(θ) + 24sin(3θ)sin(θ)
    y'' = -40cos(3θ)sin(θ) - 24sin(3θ)cos(θ)
    z'' = 0

    However I feel like i did something wrong because to computer ||v x a|| would be really messy. Is there any way to simplify before I do the cross product or is there is easier way and I'm just doing the problem wrong? Thanks any help is appreciated.
  2. jcsd
  3. Jul 8, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

  4. Jul 8, 2012 #3

    Filip Larsen

    User Avatar
    Gold Member

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook