Doughnut Calculus

  • #1
Doughnut Calculus!!!

Hey guys, I need help with a somewhat big Calculus IV problem. We are reviewing double and triple integrals in polar coordinates. So here is my problem:

Work out the mass, 2nd moment, and radius of gyration for a doughnut shaped yoyo about both [tex]x[/tex] and [tex]y[/tex] axes...

I know the following equations: mass = [tex]\iint_{D} \rho(x,y) dA[/tex]

[tex] R= {sqrt{(I/M)}}[/tex] , where I is the moment of inertia and M is the mass of the lamina (object).
Have no clue about what 2nd moment is? is this like another calculation of moments of inertia or moment about an axis?

Anyways, can someone help me get started on this one please?

Answers and Replies

  • #2
From what I recall, the 2nd moment, in physics terms, is the moment of inertia. So if you are doing it about the y-axis, you mulitply your term within the integral by x ( or r cos theta), and do the vice-versa when you are doing it about the x - axis.
  • #3
I had found that soon after I posted but thanks for replying. Still working on this one. Its a toughie.