# Homework Help: Radius of Gyration Triple integral question

1. May 18, 2010

### nugget

1. The problem statement, all variables and given/known data

By using spherical coordinates, find the radius of inertia (Is this the same as the radius of gyration?) about the z-axis of the constant density solid which lies above the upper half of the cone x2 + y2 = 3z2 and below the sphere x2 + y2 + (z-2)2 = 4. For a constant density region E of volume V, the radius of inertia about the z-axis is defined as:

VR2 = ∫∫∫(x2 + y2)dV
E

2. Relevant equations

ρ2 = x2 + y2 + z2

x = ρsin(φ)cos(θ)
y = ρsin(φ)sin(θ)
z = ρcos(φ)

mR2 = I

...where R = radius of gyration and I = moment of inertia about a given axis.

3. The attempt at a solution

At this stage I am beyond confused. Any assistance in beginning this question would be greatly appreciated.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted