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!

Solids of Revolution around y = x

  1. Feb 5, 2013 #1
    Is it possible to revolve a function around y = x? If so how would you do it?

    I suppose the main difficulty is in finding the radius for the area of a disk or cylinder. Is there any method that works will all or most functions?
     
  2. jcsd
  3. Feb 5, 2013 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi TheAbsoluTurk! :smile:

    Easiest way is to change to new coordinates p = x + y, q = x - y (or the same but divided by √2, if you prefer).

    Then x = y is the q axis, so that's just a rotation about the q axis. :wink:
     
  4. Feb 5, 2013 #3
    Ok, let's say that I'm trying to rotate y = x^2 around y = x.

    p = x + y

    q = x - y

    So do I have to insert (q + y) into x to make y = (q + y)^2 ?
     
    Last edited: Feb 5, 2013
  5. Feb 5, 2013 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Easier is to substitute x = (p+q)/2, y = (p-q)/2 :wink:
     
  6. Feb 5, 2013 #5
    Do you know of any YouTube videos or articles on the internet which show how to do this?
     
  7. Feb 5, 2013 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    uhh? :confused:

    just do it … substitute those formulas into y = x2 !​
     
  8. Feb 5, 2013 #7
    I understand that but I don't know what to do after that. Does r in ∏r^2 equal (p-q)/2? How do you integrate that?
     
  9. Feb 5, 2013 #8

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    no, the r is the distance from your axis

    your axis (originally called x=y) is the q axis, so r is the distance from the q axis, which is p (or is it p/2?)
     
  10. Feb 5, 2013 #9
    Let me get this straight:

    What is the volume of y = x^2 rotated about y = x?

    Define p = x +y

    Define q = x - y

    I don't understand why you chose to insert x = (p+q)/2 and y = (p-q)/2 ? How did you get these?
     
  11. Feb 5, 2013 #10
    Ok, I understand how you got those expressions. But what's to do next? Do you solve for p?
     
  12. Feb 6, 2013 #11

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    (just got up :zzz:)

    first you convert everything into p and q

    then you solve the problem, in p and q (you've said you know how to do this)

    finally you convert your solution back to x and y :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solids of Revolution around y = x
  1. Y^x = x^y (Replies: 3)

  2. Y^x = x^y (Replies: 20)

  3. X^y=y^x REVISITED (Replies: 3)

  4. Graph of y = x^x (Replies: 16)

  5. Solution of x^y=y^x (Replies: 2)

Loading...