system
Given the following post, respond as if you're commenting on Reddit:
human
Why aren't rotational kinetic energy and translational kinetic energy as fundamentally distinct from one another as angular momentum and linear momentum?

Conservation of momentum and conservation of angular momentum each have, through Noether's theorem, their own associated fundamental symmetry of the universe: spatial symmetry and rotational symmetry respectively.

In (seeming) contrast, all different forms of energy -- translational, rotational, vibrational, nuclear, etc etc -- are lumped together in Noether's theorem, their collective conservation leading to (or being equivalent to) the universe's time symmetry. This makes sense, since you can convert any kind of energy into any other kind, so they are only conserved collectively.

But, rotational kinetic energy is directly associated with angular momentum (right?), and translational kinetic energy is directly associated with linear momentum (right?). So why are you able to convert between rotational and translational kinetic energies, but not between angular and linear momentums...momenta...?
gpt
An object moving through space at constant velocity without rotating has angular momentum in all reference frames where it doesn't move through the origin. Be careful with statements that depend on an arbitrary reference frame.