Register to reply

Solids of Revolution around y = x

by TheAbsoluTurk
Tags: revolution, solids
Share this thread:
TheAbsoluTurk
#1
Feb5-13, 04:10 PM
P: 100
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?
Phys.Org News Partner Mathematics news on Phys.org
'Moral victories' might spare you from losing again
Fair cake cutting gets its own algorithm
Effort to model Facebook yields key to famous math problem (and a prize)
tiny-tim
#2
Feb5-13, 04:52 PM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,157
Hi TheAbsoluTurk!

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.
TheAbsoluTurk
#3
Feb5-13, 05:25 PM
P: 100
Quote Quote by tiny-tim View Post
Hi TheAbsoluTurk!

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.
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 ?

tiny-tim
#4
Feb5-13, 05:35 PM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,157
Solids of Revolution around y = x

Easier is to substitute x = (p+q)/2, y = (p-q)/2
TheAbsoluTurk
#5
Feb5-13, 05:44 PM
P: 100
Quote Quote by tiny-tim View Post
Easier is to substitute x = (p+q)/2, y = (p-q)/2
Do you know of any YouTube videos or articles on the internet which show how to do this?
tiny-tim
#6
Feb5-13, 05:49 PM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,157
uhh?
just do it substitute those formulas into y = x2 !
TheAbsoluTurk
#7
Feb5-13, 05:53 PM
P: 100
Quote Quote by tiny-tim View Post
uhh?
just do it substitute those formulas into y = x2 !
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?
tiny-tim
#8
Feb5-13, 06:01 PM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,157
Quote Quote by TheAbsoluTurk View Post
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?
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?)
TheAbsoluTurk
#9
Feb5-13, 06:26 PM
P: 100
Quote Quote by tiny-tim View Post
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?)
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?
TheAbsoluTurk
#10
Feb5-13, 08:17 PM
P: 100
Quote Quote by TheAbsoluTurk View Post
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?
Ok, I understand how you got those expressions. But what's to do next? Do you solve for p?
tiny-tim
#11
Feb6-13, 02:04 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,157
(just got up )

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


Register to reply

Related Discussions
Solids of Revolution Calculus & Beyond Homework 3
Solids of revolution Precalculus Mathematics Homework 3
Solids of revolution Calculus & Beyond Homework 3
Solids of Revolution Calculus & Beyond Homework 2
Solids of revolution Calculus 5