If you are holding the wheel at the same angle in a car, why does speeding up or slowing down change the radius of your turn?

Question

I generally feel like I can figure things out, but this has just always kept me stumped. A good example is going up or down one of those screw-shaped parts of some parking garages. You can find the correct angle for your speed, but if you slow down or speed up without changing the wheel, the turn becomes sharper or wider.

Why?

In: Physics

Answer 1

Because tires don’t grip perfectly. There’s some scrub which is exaggerated with more speed.