56CHAPTER 1. INTRODUCTION1.49Chapter 1, Problem 49Problem:Using the relations between coordinates and unit vectors in Cartesian and cylindri-cal coordinates, compute the velocity components in Cartesian coordinates for a general vectorV=Vrer+Vθeθ+Vzk. Use your results to transformV=Ωreθ.Solution:The relation between unit vectors in Cartesian and cylindrical coordinates iser=icosθ+jsinθ,eθ=−isinθ+jcosθ,k=kHence, the vectorVisV=Vr(icosθ+jsinθ)+Vθ(−isinθ+jcosθVzk=(Vrcosθ−Vθsinθ)i+(Vrsinθ+Vθcosθ)j+Vzk=Vxi+Vyj+VzkTherefore, the velocity components transform according to
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 10/15/2010 for the course AME 301 at USC.