A wheel (or any ring of considerable mass) hardly balances itself when it is placed vertically on ground, but when we roll it along the ground it balances itself. What causes this effect? I guess its because of the centrifugal force generated by the circular motion of the wheel that makes the outer surface of the wheel rim to stick to the ground, but I am unsure whether this is the correct explanation.
Just like Anna V said, Conservation of angular momentum. It's sort of like how on Motorcycle races the racer's can do extremely sharp turns with their knee's almost touching the the ground. Once it's gained enough speed it begins to just well, support itself. (I understand that is a very bad word to use for this question but it's hard to explain)
Physics is the accumulation of observations, the devising and fitting mathematical models to these observations and study of the predictions of the mathematical models to validated them.
In the progress of time, the mathematical models become theories, i.e. derived from a few postulates, also called laws, that define the framework for physical problems , and there can be very general predictions from these mathematical models, called conservation laws.
There is the conservation of energy, the conservation of momentum and the conservation of angular momentum in kinematics problems that are directly provable mathematically starting from the laws of mechanics.
Ultimately conservation laws are directly dependent on observations and experiments. They are the distillation of innumerable observations, fitted mathematically.
In this sense asking why a wheel does not fall is like asking why is there conservation of energy.
The wheel does not fall because the angular momentum it has gained has to be dissipated/transferred by interactions , and the interactions of a wheel are with the ground at a very small point which can absorb by friction only small quantities of angular momentum. (air is not very efficient in braking unless of hurricane force). In a similar way a rolling ball even on a flat ground, can travel a long way because it can only lose momentum and energy through the small point like area with the ground.