- #1
ChemistryJack
- 3
- 0
Hi, one of my vac work questions is:
A lamina has density d(x,y) = x^2 + y^2 and is defined by -2<x<2 ; -3<y<3. Calculate the moment of inertia about an axis perpendicular to the lamina through the point (1,1).
I'm confident that I find Ix which is equal to the double integral of the density multiplied by y^2 and Iy which is equal to the double integral of the density multiplied by x^2 and add them. However, it's the limits that I'm unsure of, because for a similar question before, I integrated using the dimensions of the lamina, and my tutor said my limits should be different, I know it has something to do with the fact the moment of inertia is taking place at a given point. Could someone please help me with my limits?
Thanks a lot, also I apologise if it's difficult to read because I don't know how to write the symbols etc. properly online.
A lamina has density d(x,y) = x^2 + y^2 and is defined by -2<x<2 ; -3<y<3. Calculate the moment of inertia about an axis perpendicular to the lamina through the point (1,1).
I'm confident that I find Ix which is equal to the double integral of the density multiplied by y^2 and Iy which is equal to the double integral of the density multiplied by x^2 and add them. However, it's the limits that I'm unsure of, because for a similar question before, I integrated using the dimensions of the lamina, and my tutor said my limits should be different, I know it has something to do with the fact the moment of inertia is taking place at a given point. Could someone please help me with my limits?
Thanks a lot, also I apologise if it's difficult to read because I don't know how to write the symbols etc. properly online.