vjk2 said:
if I spinned a flat blade (eg: no lift) clockwise it should go up, and counterclockwise it should go down in accord with what I've been taught so far about the cross product as it relates to statics. Does this occur?
Off hand this doesn't make sense. But the math seems to suggest it...
I think you might be referring to the
angular velocity unit vector. But this doesn't mean that the blade (or any other object) is going to necessarily
move in that direction. Rather the direction of angular velocity is merely a convention.
Angular velocity has a direction which is perpendicular to the instantaneous velocity of any point on the object that is actually spinning. In other words, the angular velocity points along the axis of spin. But there still needs to be some convention about which way, along the axis (up or down), the vector points.
There is a convention called the "right hand rule" that says if you put your fingers along the direction of spinning, such that spinning starts at your hand and works its way out to your fingertips, then your extended thumb points in the direction of the angular velocity vector. But this is just a convention.
Hypothetically, the convention could have just as easily been defined using the "left hand rule" such that the angular velocity's direction is always defined using the left hand. If that rule were made instead, and it was
consistently also applied to angular acceleration, torque, and everything related, all the final answers would come out
the same in the end, although some of the intermediate answers (things still in terms of angular velocity, torque, etc.) might have different signs.
But to ensure that you get the same intermediate answers that your instructor/text book expects, make sure you use the right hand rule (not the left hand rule). Angular momentum, angular velocity, angular acceleration, and torque are all
defined using the right hand rule. Just realize that it's nothing more than a well established
convention.
(By the way, as you've described it, the right-hand-rule applies to your particular blade analogy, only if you are below the blade, looking up at the whole thing.)
