What is the conjugate variable of angular momentum?

We know that for Heisenberg uncertainty principle, position and momentum are conjugates, energy and time are conjugates. Like wise what is the conjugate variable for angular momentum? Is it orientation along with something? Or anything else?

P.Q:-Another observation, the unit of Angular momentum already is kg*m^2/s, which is supposed to be the unit of uncertainty. So the conjugate variable must be unit less

• Be careful about using the HUP with angular momentum and putative "conjugate" coordinates. See physics.stackexchange.com/a/338057/36194 and physics.stackexchange.com/a/354397/36194 as there is no legitimate angle operator. Commented Sep 2, 2018 at 21:20
• @ZeroTheHero Does the HUP not apply to angular momentum? Commented May 1 at 8:00
• @Wookie HUP applies to two angular momentum generators, but - say - $L_x$ and $L_y$ are not conjugate observables so these are not the same as an angle and an angular momentum as implied by OP. Commented May 2 at 12:36

In the same way that the conjugate of linear momentum is position ($x$), the conjugate of angular momentum is "angular position", a.k.a. orientation. You can find a list of other conjugate pairs here.