Right hand grip rule in rotational kinematics

[fterh]

Simple question: Is there a reason behind the right hand grip rule, or is it just like that (inexplicable)? How do we know that for an object with counter-clockwise rotation (e.g. on the table), the angular velocity is upwards?

 

[Yuqing]

It is generally defined that way to be consistent with the mathematical conventions of the cross product.

 

[Andrew Mason]

Simple question: Is there a reason behind the right hand grip rule, or is it just like that (inexplicable)? How do we know that for an object with counter-clockwise rotation (e.g. on the table), the angular velocity is upwards?

Just to add to what Yuqing has said, it is evident that to describe angular motion, one has to describe the plane in which the rotation occurs at a given time. Once it was seen that the perpendicular axis of rotation can be used to assign a unique direction to the angular motion, it was then a completely arbitrary choice as to which of the two possible directions to assign to the rotational motion. It was decided that the convention would be to assign the direction of the angular velocity vector according to the right hand rule.

AM