Today's lecture in intro mechanics is a whirlwind survey of vectors. While I struggle to clear my head enough to be able to teach this stuff, here's a Dorky Poll to pass the time:
This is a strictly classical subject, so please choose only one.
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Doesn't this depend on what you're doing? Whether Cartesian vs. Polar variants are the more appropriate depends on the problem you're trying to solve if my extremely rusty calculus isn't leading me astray.
Personally, I prefer ECEF or ENU, depending on the problem.
Parabolic, for the Stark effect.
I usually don't have to worry about a radius, but spherical is the only way to go - stereonets rule!
In the interest of full disclosure, I'm a structural geologist and a fondness for such things is an occupational hazard.
Though usually I work in 2 dimensions and let the contractor sort out the 3rd (as there are standards that govern it they can't really do it wrong).
You missed an option: I object to the poll, because I have the sense to pick a coordinate system appropriate to the situation :-P
Eddington-Finkelstein-coordinates of course!
You definitely want to use spherical coordinates when doing projectile motion with a = -g j-hat ...
I object to this poll because the radial coordinate in cylindrical geometry is _s_, not r.