The three unit vectors r and which describe spherical

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f a particle in polar ˆ coordinates to spherical coordinates (4 pts each lettered part). The three unit vectors: r, θ and φ which ˆˆ describe spherical coordinates can be written as: ˆ r = sin θ cos φˆ + sin θ sin φˆ + cos θk, ˆ i j ˆ ˆ θ = cos θ cos φˆ + cos θ sin φˆ − sin θk, i j ˆ φ = − sin φˆ + cos φˆ i j. (3) (4) (5) (a) Let’s investigate that the definitions given in Eqs.(3-5) make sense. First, define in your own words ˆ what orthonormal vectors are, and then check to see if these vectors r, θ and φ are orthonormal. Then, ˆˆ convince yourself (and the grader) that e.g. at least the x-component of r is correct, using a simple ˆ geometric picture. (Taylor’s Fig 4.16, or Boas Fig 4.5 should help) (b) If the particle is constrained to move with φ = 0, state in simple words what this means in terms of the particle motion. Sketch the three spherical unit vectors at some point φ = 0 and r = R for some particular (nonzero) angle θ of your choice. (c) Show that the velocity of any particle in spherical coor...
View Full Document

This document was uploaded on 03/09/2014 for the course PHYSICS 2210 at Colorado.

Ask a homework question - tutors are online