So heres the question:(adsbygoogle = window.adsbygoogle || []).push({});

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 :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Quick question with spherical coordinates and vectors

**Physics Forums | Science Articles, Homework Help, Discussion**