Hello everyone, I have some conceptual problems understanding the rotating frame transformation. Take the center of the Earth as inertial frame's origin and another point in Hawaii as rotating frame's origin. In many lecture notes from internet, or Marion chapter 10. The vector describing the rotating frame is ω, which is pointing upward to the north pole of the Earth. However, if we think the angular velocity of rotating frame's origin as r×v. It is not directly pointing to North pole and shifted some amount. I have read the wiki page and it used ω = r×v v = ω×r simultaneously, which confuses me a lot ! Can someone help me clear the concept? I believe the answer should be ω is point to north pole in the transforming equations but what is wrong with ω in ω = r×v ? This is the definition of angular veolcity but it seems does not match the ω in the frame transforming equations. Thanks for you help.