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#### etotheipi

The Wikipedia page for angular velocity makes a big fuss over "spin" and "orbital" angular velocities, but I have checked through Gregory and Morin's textbooks on classical mechanics and haven't found any reference to them at all. They just work with a single quantity, the

Alarmingly, Wikipedia says that the "orbital" angular velocity is dependent on the choice of origin. That immediately seemed odd, since those other two sources both defined ##\vec{\omega}## w.r.t. the instantaneous axis of rotation of the particle/rigid body, which should be invariant under translations (unlike the angular

I wondered if Gregory and Morin are

*angular velocity*.Alarmingly, Wikipedia says that the "orbital" angular velocity is dependent on the choice of origin. That immediately seemed odd, since those other two sources both defined ##\vec{\omega}## w.r.t. the instantaneous axis of rotation of the particle/rigid body, which should be invariant under translations (unlike the angular

*momentum,*which is evidently dependent on origin). Furthermore, this notion of "orbital angular velocity" doesn't seem to satisfy any of the theorems given for angular velocities in those texts (e.g. addition of angular velocities in different reference frames, etc.)I wondered if Gregory and Morin are

*always*referring to spin angular velocities? And if so, is there ever any need for the "orbital" variety of angular velocities? Thanks!
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