homework2

# The three unit vectors r and which describe spherical

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

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