When your arms are extended, your rotational inertia is relativly large. As you slowly turn, your angular momentum is the product of rotational inertia and rotational velocity. When you pull your arms in, the rotational inertia of your body is reduced. This causes your rotational velocity to increase, making you spin faster. The earth is round because of gravitation.
Masses attract other masses, and so the earth has attracted itself together as far as it can.
As a result, every part of the surface is equidistant form the center of gravity, which creates a sphere. There is no such force in a nonaccerlated reference frame. Well, now that you understand that this is not due to the imaginary centrifugal force, I shall explain. While inertia is not a force, it is a body's natural resistance to change. In this scenario, the car's inertia is causing it to attempt to travel straight, thus resisting the curve and sliding.