257_Problem CHAPTER 9

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

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

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,
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