Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I know they mean "rotate this way" and "rotate that way," respectively, but is there a standard name for "rotational direction?"

"omega" often measures the angle, but what variable name usually designates the direction of rotation?

(I'm naming variables for my program that will have to rotate things in a Cartesian plane)

share|improve this question
With the winding number in various manifestations in math, positive is anti or counterclockwise, negative is clockwise. We may or may not have complex numbers to thank for this convention. –  anon Sep 6 '11 at 1:27
Northern Hemisphere, or Southern? –  Gerry Myerson Sep 6 '11 at 2:49
Gerry, Southern hemisphere, but we're actually on Venus, so it's like your Northern hemisphere. –  Thunder Rabbit Sep 6 '11 at 3:02
FWIW: I wanted to give you additional marks for mentioning Venus. It rotates in the opposite direction as Earth, so the clever North/South play is really, very clever. Hip Hip. –  mixedmath Sep 6 '11 at 3:26
Are you too young to remember analog clocks? That is the source. –  Ross Millikan Sep 6 '11 at 3:33
show 4 more comments

2 Answers

up vote 0 down vote accepted

May be you should read this.http://www.xamplified.com/positive-and-negative-angles/

*As per my understanding of "rotate this way" and "rotate that way" you are referring to terminal sides above and below the x-axis.When i first took trig this is what i was taught. *

share|improve this answer
Though it turns out my original question was made moot by not needing to create the unnamed variable in the first place, this answer most closely answers my moot question. –  Thunder Rabbit Sep 8 '11 at 4:59
add comment

As I've always understood it, the idea comes from the cross product and angular momentum. If we can agree on an 'up' direction (the positive z axis in a coordinate plane), then we say a rotation is positive if the direction of its angular momentum, as determined by the right hand rule, is upward (that is, has any positive z component). This does end up agreeing with the winding number argument - counterclockwise in the xy plane is positive.

As I type this, it makes me wonder - what if it's perpendicular to the z axis? Well, I don't know. I suppose I'm out of luck. But such strange times might call for strange measures, and we could actually describe the angular momentum vector to remove all doubt - or we could just change coordinates so that 'up' isn't quite how we thought of it before.

share|improve this answer
"or we could just change coordinates so that 'up' isn't quite how we thought of it before." - hence Gerry's comment. :D –  J. M. Sep 6 '11 at 3:21
In this case, the animations are on a Cartesian plane, so I don't have to worry about "exotic" (haha) rotations for anything other than within the plane. –  Thunder Rabbit Sep 8 '11 at 4:56
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.