1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quick question with spherical coordinates and vectors

  1. Sep 27, 2011 #1
    So heres the question:
    An ant crawls on the surface of a ball of radius b in such a manner that the ants motion is given in spherical coordinates by the equations:
    r = b, [itex]\phi[/itex] = [itex]\omega[/itex]t and [itex]\vartheta[/itex] = [itex]\pi[/itex] / 2 [1 + [itex]\frac{1}{4}[/itex] cos (4[itex]\omega[/itex]t).

    Find the speed as a function at time t and the radial acceleration of the ant.

    I found the speed, doing [itex]\left|v\right|[/itex] = b[itex]\omega[/itex][cos[itex]^{2}[/itex]([itex]\frac{\pi}{8}[/itex]cos 4[itex]\omega[/itex]t) + [itex]\frac{\pi^{2}}{4}[/itex] sin[itex]^{2}[/itex] 4[itex]\omega[/itex]t] [itex]^{1/2}[/itex]

    Now I don't even know where to begin to take the derivative of that, lol. I know i derive the actual vector v, not the magnitude of it. But how do i derive e[itex]_{\phi}[/itex] and e[itex]_{\vartheta}[/itex]?

    I got for velocity

    v = [itex]\widehat{e}[/itex][itex]_{\phi}[/itex]b[itex]\omega[/itex]cos [[itex]\frac{\pi}{8}[/itex]cos 4[itex]\omega[/itex]t] - [itex]\widehat{e}[/itex][itex]_{\vartheta}[/itex]b[itex]\omega[/itex] [itex]\frac{\pi}{2}[/itex]sin (4[itex]\omega[/itex]t)

    Any help on deriving that to find acceleration would be awesome :s Maybe I'm missing a rule with [itex]\widehat{e}[/itex][itex]_{\phi}[/itex], but I'm getting stuck.

    Thanks :)
     
  2. jcsd
  3. Sep 28, 2011 #2
    Any help would be greatly appreciated.
     
  4. Sep 28, 2011 #3

    ehild

    User Avatar
    Homework Helper
    Gold Member

    See: http://en.wikipedia.org/wiki/Spherical_coordinate_system,

    "Kinematics"

    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Quick question with spherical coordinates and vectors
Loading...