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when first learning about the angular velocity/acceleration, the right hand rule is mentioned. According to it, the direction of angular velocity/acceleration is along the axis perpendicular to the plane of rotation. However at first glance this is not so intuitive. This got me to wonder if such direction of such vector is mathematical construct people made to make things convenient, or if it is a description of something intrinsic in workings of the universe. In other words, in certain situations, could the direction of angular velocity/acceleration affect physical system along that direction? Thanks

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When rotational properties are defined as vectors, those vectors represent the axis we are rotating about. But the vector direction is a mathematical invention without much physical meaning. It gives us consistent rules for eg the cross product (another mathematical invention), but has no intuitive meaning.

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  • $\begingroup$ What about the gyroscopic precession? the direction of torque perpendicular to the plane of two perpendicular vectors r and and weight causes the change in angular momentum of the gyroscope. So the direction of torque arising from the right hand rule seem to have physical implications, no? $\endgroup$ – Patrick Oct 7 '19 at 4:40
  • $\begingroup$ @Patrick Yes, precession is indeed a counterintuitive phenomenon. But the imagined vector form of a rotational quantity is nevertheless still a man-made invention. The right-hand rule is also a man-made invention, and it is all made to fit together. Even a man-made mathematical invention or imagination can be useful because it makes it easier for us to understand the directions and axes involved. I am not sure that qualifies as "having physical implications". $\endgroup$ – Steeven Oct 7 '19 at 5:42

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