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Spherical Vector Addition Process

  1. Aug 5, 2011 #1
    Hello Everyone,

    I was just wondering if there was a way to add two vectors that are determined by spherical coordinates (radius, theta, phi). For example, if I have v1 = (5, Pi/4, Pi/2) and v2 = (3, Pi, -Pi/2) is there a way to add these using their respective radii, thetas, and phis or do I HAVE to convert them to Cartesian coordinates first, perform the addition, and then convert back?

    Also, if anybody knows, what is the difference between "bound" and "free" vectors? I was looking around and this came up but the description was a bit fuzzy.

    Thanks again!
  2. jcsd
  3. Aug 5, 2011 #2


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    hello n00bcake22! :smile:
    there's probably a way of doing it once you've found the angle between the two vectors

    but converting to Cartesian is the only easy way :smile:
    a free vector is like velocity … you can slide it about anywhere, especially when you want to add it to another vector

    a bound vector is like force … you can't slide it about unless you compensate by adding a couple … a bound vector is really a pair, the vector itself and the line of application :wink:
  4. Aug 8, 2011 #3
    Thanks tiny-tim!

    Converting to Cartesian and back it is! :) Is this the suggested method for all vector operations (dot/cross product, etc.)?

    Could you give a slightly more verbose example of “bound” and “free” vectors? I am still a bit confused.

    Using your examples, a force A i^ + B j^ + C k^ (bound?) is acting on a point mass M whose velocity is D i^ + E j^ + F k^ (free vector?). I fail to see the difference. :(
  5. Aug 8, 2011 #4


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    hi n00bcake22! :smile:
    yes (except for very simple cases)
    we don't usually want to add velocities …

    although we often add the force on two different points, or the momentum of two different points, we never have any reason to add the velocities of two different points …

    but we do add relative velocities, and when we add them the line through which they act doesn't matter, so velocity is a free vector :wink:
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