Is angular frequency absolute?

[tade]

In classical mechanics, is the angular frequency of a rotating object, planetary system etc. the same as viewed from any inertial reference frame?

 

[mfb]

All reference frames can agree on a common clock, and all frames have a meaningful way to assign a direction to the object.
They have to agree on the center of rotation, but that should be easy for rotating solid objects, planetary systems and so on.

 

[0xDEADBEEF]

The key to the answer is whether the centre of rotation is part of your reference frame. If two objects circle each other around their common centre of mass the angular frequency of this rotation is independent of the inertial reference frame. If, on the other hand, you consider rotations around the origin of your coordinate system (something that is usually done in conservation of angular momentum calculations) then the instantaneous angular frequency will depend on the inertial reference frame.

 

[tade]

The key to the answer is whether the centre of rotation is part of your reference frame. If two objects circle each other around their common centre of mass the angular frequency of this rotation is independent of the inertial reference frame. If, on the other hand, you consider rotations around the origin of your coordinate system (something that is usually done in conservation of angular momentum calculations) then the instantaneous angular frequency will depend on the inertial reference frame.

I understand. thanks

 

[sardar]

In classical mechanics, angular frequency is defined as the rate of change of angular displacement of a rotating object and is measured in radians per unit of time. It is a fundamental property of a rotating system and is independent of any specific reference frame.

Therefore, angular frequency can be considered absolute in the sense that it remains constant regardless of the observer's frame of reference. This is in contrast to other quantities, such as velocity or acceleration, which are relative and depend on the observer's frame of reference.

In other words, the angular frequency of a rotating object will be the same when viewed from any inertial reference frame. This is due to the fact that the laws of physics, including the principles of rotational motion, are the same in all inertial reference frames.

However, it is important to note that in the realm of relativity, where objects are moving at speeds close to the speed of light, the concept of angular frequency may become more complex and may not be absolute. In these extreme cases, the laws of physics may be affected by the observer's frame of reference.

Overall, in the context of classical mechanics, angular frequency can be considered an absolute quantity that remains constant regardless of the observer's frame of reference.