256_Problem CHAPTER 9

256_Problem CHAPTER 9 - PROBLEM 9.176 For the right...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PROBLEM 9.176 For the right circular cone of Sample Prob. 9.11, determine the value of the ratio a / h for which the ellipsoid of inertia of the cone is a sphere when computed ( a ) at the apex of the cone, ( b ) at the center of the base of the cone. SOLUTION ( a ) From sample Problem 9.11, we have at the apex A 2 3 10 x I ma = 22 31 54 yz I Im a h  == +   Now observe that symmetry implies 0 xy yz zx III === Using Equation (9.48), the equation of the ellipsoid of inertia is then 222 1 xyz Ix Iy Iz + += or 2 2 2 2 2 2 33 1 3 1 1 1 0 ma x m a h y m a h z + ++ For the ellipsoid to be a sphere, the coefficients must be equal. Therefore, 2 1 10 5
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online