Let 0 < a < 1, 0 ≤ b < 1 and I = [0, 1). We call contracted rotation the interval map φ_{a,b}: x ∈ I → ax+b mod 1. Once the parameter a is fixed, we are interested in the family φ_{a,b}, where b runs on the interval I. We use the fact that, as in the case of circle homeomorphisms, any contracted rotation φa,b has a rotation number which depends only on the parameters a et b. We will discuss the dynamical and diophantine aspects of the subject.