257_Problem CHAPTER 9

257_Problem CHAPTER 9 - PROBLEM 9.177 For the homogeneous...

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

View Full Document Right Arrow Icon
PROBLEM 9.177 For the homogeneous circular cylinder shown, of radius a and length L , determine the value of the ration a / L for which the ellipsoid of inertia of the cylinder is a sphere when computed ( a ) at the centroid of the cylinder, ( b ) at point A . SOLUTION ( a ) From Figure 9.28 ( ) 22 2 11 3 21 2 xy z I ma I I m a L == = + Now observe that symmetry implies 0 xy yz zx III = Using Equation (9.48), the equation of the ellipsoid of inertia is then ( ) ( ) 222 2 2 2 2 2 2 2 1 1: 3 3 1 2 1 2 xyz I xI yI z m a x m aL y m ++= + + + + = For the ellipsoid to be a sphere, the coefficients must be equal. Therefore,
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/11/2011 for the course EGM 2511 taught by Professor Jenkins during the Spring '08 term at University of Florida.

Ask a homework question - tutors are online