you don't calculate w.. it's a status. You have your status at t0 and you are calculating your new status at t1. Wheel angular velocity is part of the status t0.
once you calculate all the forces on the system you integrate it and w is part of your result, that becomes the input status for your next iteration.
Okay... this may sound silly but that simple paragraph supposes a lot of clarification to me. I'm using Unity 3D, so I'm constrained to a subset of the physics engine (PhysX). No access to the integrator at all - only rigidbody dynamics that just work and the ability of applying forces to it (rigidbody.AddForceAtPosition).
But it doesn't mean that I'm trying to solve a nonexistent problem. Now I have a much better picture of the problem I'm working on, and it has to do with another of your replies:
Sadly, to be a good car simulator developer you need to invest lots of money trying to acquire every available book and paper on the matter. I have a huge library with references to interesting graphs and formulas all collected so I can easily find what I need when I need it. Once you start seeing tyre curves from different sources you start to see patterns and things like tyre models just become tools for you to reproduce those patterns. I don't think those tyres pacejka sets commonly found on the internet are a good starting point to develop a sim at all. I strongly suggest you to start your journey getting the Tyre Dynamics book from Mr. Pacejka himlself.. at least you'll understand what kind of trip you have ahead of you (and get good data to start with).
My goal is to develop the most realistic vehicle simulation that could be achieved only with the minimum (and simplest) math involved. Of course, it wouldn't be comparable to the high-end solutions, but it will provide developers a rather simple method that could be easily understood, implemented, and tuned for each specific project. Thus, developers with limited physics knowledge (as me) could still develop good vehicles that would be realistic enough for most projects.