Why atoms do not radiate energy? In atoms electron moves in a circular motion with constant velocity but in circular motion acceleration is produced when we change direction so we cant get constant velocity.
So why electron do not emit energy when they revolve
 A: The question, intended as "what is the reason why electrons don't lose energy" has a short answer: because they don't. 
With this I mean that, according to the Bohr's model, this is just how electrons behave. They do not lose energy when they are on a particular energy level (or, improperly, orbit), they do so when they are changing the orbit. 
Asking this question would be somehow similar to asking why gravity is attractive instead than repulsive: and the answer is "because that's how gravity works". Obviously the electron situation is different because we know that, in general, a non quantum system like that one should indeed lose energy, but the answer is still "because that's how electrons work". 
A more "proper" question that one could ask is "why don't electrons lose energy" meaning "could they do it? Why aren't we observing it?" is still very open, and brings up subjects like the mutiverse, where other universes could have laws of physics that make the electron lose energy, for example.
Edit: what I said is the second postulate of Bohr, and being a postulate is something that we "observe and describe" without further reasoning. We observe that the electron doesn't lose energy? Then they don't lose energy. We observe that the gravitational force is attractive? Then the gravitational force is attractive. There may be a point in the future, if we find out that even the electron isn't a fundamental particle, when we'll be able to transform the postulate in a proof, but this is not the moment yet. Same stands for gravity.
