- #1

aligator11

- 10

- 0

- Homework Statement
- Evaluate the Moment of Inertia with respect to Oz axis of the [...] solid A: (x^2+y^2+z^2)^2<=z

- Relevant Equations
- Formula for moment of inertia: Iz=SSS(x^2+y^2)*constant-density*dxdydz

Cylinder Jacobian: SSS(x,y,z)*|r|dθdrdφ

Cylinder Jacobian substitution parameters:

x=rsin(θ)cos(φ)

y=rsin(θ)sin(φ)

z=rcos(θ)

Jacobian -->|r|=r^2*cos(θ)

Hello everybody.

If anyone could help me solve the calculus problem posted below, I would be greatful.

Task:

Bounded by area - A: (x^2+y^2+z^2)^2<=zSo far I was able to expand A: [...] so that I receive something like this: r=(cos(θ))^(1/3) for the definite intergral of my radius. I'm not sure what is the next step I should take...

Thank you all the great souls which are able to help me in that matter.

Cheers!

If anyone could help me solve the calculus problem posted below, I would be greatful.

Task:

**Evaluate the moment of inertia with respect to Oz axis of the homogeneous solid A**Bounded by area - A: (x^2+y^2+z^2)^2<=zSo far I was able to expand A: [...] so that I receive something like this: r=(cos(θ))^(1/3) for the definite intergral of my radius. I'm not sure what is the next step I should take...

Thank you all the great souls which are able to help me in that matter.

Cheers!