Is My Approach to Solving the Inertia Tensor of a Rotating Cone Correct?

[Saxonphone]

Homework Statement

From Goldstein's Classical Mechanics (Chapter 5 - Exercice 17 - Third Edition)
A uniform right circular cone of height h, half angle A, and density B rolls on its side without slipping on a uniform horizontal plane in such a manner that it returns to its original position in a time t. Find expressions for the kinetic energy and the components of the angular momentum of the cone.

The Attempt at a Solution

Well, first of all, I found the inertia tensor for a cone with the z axis along the axis of symmetry of the cone and the origin at his apex, then I made it "rotate" (90-A) degrees to put the x-axis in the line of the cone's surface that is always in contact with the plane (a drawing would be good I know, but...)

The tensor is diagonal and what i found was

As the angular velocity w( vector) always lies in that line, so one can say w (vector) = w(cosA k - sinA i) where w is the modulus of the vector and i and k the unit vectors of x and z.
w can be found with the data provided and is given by

Knowing all this, all I have to do is put what I got in L (vector)= I (tensor) w (vector) and T=1/2 I w^2.

The book got no anwers, so, anything wrong with what i did?

 

[the_kid]

I realize this is an old thread, but I'm working on this problem and am in a similar place as Saxonphone was. Does this look correct, so far?