p0172 - 1.72. CHAPTER 1, PROBLEM 72 79 1.72 Chapter 1,...

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1.72. CHAPTER 1, PROBLEM 72 79 1.72 Chapter 1, Problem 72 Problem: Using the relations between coordinates and unit vectors in Cartesian and cylindri- cal coordinates, compute the velocity components in cylindrical coordinates for a general vector V = V x i + V y j + V z k . Use your results to transform V = V j . Solution: The relation between unit vectors in Cartesian and cylindrical coordinates is i = e r cos θ e θ sin θ , j = e r sin θ + e θ cos θ , k = k Hence, the vector V is V = V x ( e r cos θ e θ sin θ )+ V y ( e r sin θ + e θ cos θ V z k =( V x cos θ + V y sin θ ) e r +( V x sin θ + V y cos θ ) e θ + V z k = V r e r + V θ e θ + V z k Therefore, the velocity components transform according to
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This note was uploaded on 05/11/2011 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.

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