Angular velocity can be given in rad/s. No one will bat an eye if you do that. It’s even recommended. But it’s not a unit in the same sense than the other ones.
but I’m the user, I want the definitions to cater to me and describe my world. I want my definitions-based logic to make sense. And if torque is defined as joules but shows up as J/rad in the UI, then who supplies the /rad except an additional definition for a contradiction or exception? My conclusion from that is that the definition is missing something shaped like a base dimension for angle.
You’re conflating UI and definitions.
Angular velocity can be given in rad/s. No one will bat an eye if you do that. It’s even recommended. But it’s not a unit in the same sense than the other ones.
but I’m the user, I want the definitions to cater to me and describe my world. I want my definitions-based logic to make sense. And if torque is defined as joules but shows up as J/rad in the UI, then who supplies the /rad except an additional definition for a contradiction or exception? My conclusion from that is that the definition is missing something shaped like a base dimension for angle.