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: Parametric equations

  1. Oct 9, 2006 #1
    Let L be the circle in the x-y plane with center the origin and radius 57.
    Let S be a moveable circle with radius 30 . S is rolled
    along the inside of L without slipping while L remains fixed.
    A point P is marked on S before S is rolled and the path of P is studied.
    The initial position of P is (57,0).
    The initial position of the center of S is (27,0) .
    After S has moved counterclockwise about the origin
    through an angle t the position of P is
    x= 27 \cos t + 30 \cos \left( \frac{9}{10} t \right)
    y= 27 \sin t - 30 \sin \left( \frac{9}{10} t \right)
    How far does P move before it returns to its initial position?
    Hint: You may use the formulas for cos( u+v) and sin( w /2).
    S makes several complete revolutions about the origin before P returns to (57,0).

    I tried taking the derivative of the x and y equations, each squared and added together and took the square root of that sum from 0 to 57. Apparently that was the wrong method, but I was wondering how I could go about doing this problem.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted