Is the direction of rotation vector is convention? Rotation vector is along the axis of rotation and is given by right hand rule. As much I understand, rotation can be clockwise as well as anticlockwise, in other words it has direction. So it can(or should?) be represented by a vector. Direction of rotation vector is given by right hand rule. Is this just some sort of convention or is there any scientific reason for this? Why not left hand  or any other rule?
 A: This answer is originally from Quora.

It is in fact a convention, and it can be avoided by using the correct
  algebraic objects.
If a wheel is spinning clockwise, whether you choose to represent its
  angular momentum as pointing away from you (right-hand rule) or toward
  you (left-hand rule) doesn't change the reality of how it's actually
  rotating, which is clockwise. In other words, quantities whose
  direction depend on the arbitrary choice of right-hand or left-hand
  rule simply are not observable at all. Observable quantities are
  always independent of handedness convention.
A good example comes from electromagnetism. To assign a direction to
  the magnetic field around a current-carrying wire, you need the
  right-hand rule. And in order to determine the force on a parallel
  current-carrying wire due to this field, you need to apply the
  right-hand rule again. But if all you do is observe the force, and
  ignore the magnetic field for a moment, the result you'll observe is
  independent of handedness: if the current travels in the same
  direction in the two wires then they are attracted, and if it travels
  in opposite directions then they are repelled. This, you can observe
  directly; the magnetic field, you cannot.

More reading:
Brian Bi's answer to What is a pseudovector?
A: Yes, it is a convention. We have to pick a positive and a negative side, so we picked the right hand rule.
This is just like we picked that the Z axis points in such a way that when facing X-Y from the usual point of view, Z grows positive "away from the paper".
(Notice that I didn't mention the choice of X or Y axis in the same way. We arbitrarily choose which way we draw the X and Y axis, but we don't choose which way they "go" the way we choose the way the Z axis "goes". It's not hard to see that you can draw the X and Y axis in any direction of your choice by simply changing the observer's vantage point and angle, without changing anything else. E.g. by "looking from behind" or "Upside-down". However the Z axis has to be "picked arbitrarily", because you can't flip it just by changing your vantage point. You would be forced to apply a reflection.)
Notice also that there are only two choices for the rule: right-hand rule or left-hand-rule. the choice has to be consistent, and you can only choose which way the arrow goes: "that way", or "the opposite way". There is no "any other rule" available.
