The real answer has a lot less to do with physics and a lot more to do with politics.
The real answer involves lock to lock steering rations, friction coefficients of tires, downdrafts, and car weights. But cars are all different with different levels of drivers. Yes, different levels of drivers. If you can’t figure out how to parallel park why do you think you can take a high-speed maximum turn at a 100mph? And even if you can parallel park you can probably only do that turn if you have been professionally trained.
Most roads are speed defined either by traffic load or by turn speed. Typical streets are just classified as (highest to lowest) highway, arterial, collector, and street. Most municipalities just post a value based upon that designation.
Turns are more important when it comes to design speed.
The tightest turn expected to be taken by “composite passenger vehicle” is a 20-foot interior radius. And you need to be moving at about 2–3mph to make it. Think of a drive-through aisle with a u-turn. That would be a fair idea of the tightest possible turn.
On the other end we have freeways. Rumor has it that speeds of between 130–160mph were used to design the sharpest inside-most turns. Keep in mind that this is the freeway itself and not on or off ramps. In speaking with Caltrans engineers, they seem to feel that this is more of rumor that may have had some truth at one point, but now turns are more related to the realities of property acquisitions and whether the turns conform with general empirical models based on the existing freeway system.
In between these we have the posted speed turn. Again, most of this is based on empirical models released from Caltrans and the Federal Highway Administration, but the posted speed tends to be about half of the speed the turn is rated for unless the local municipality has decided to reduce it further. Again, don’t go thinking that this means you can take the turn at double the speed. You are more likely to lose control or spin your vehicle without a lot of training. And even that requires that your vehicle was set up correctly for a turn like that.
Please don’t speed through turns. You can easily kill yourself and others in a blink of an eye.
