  The observations of W UMa type stars show a well-defined short-period limit
of 0.22 d, which is equivalent to a lower mass limit of approximately 1 solar
mass for the total binary mass. It is currently believed that cool contact
binaries are formed from detached binaries losing angular momentum (AM) via a
magnetized wind. Orbital evolution of detached binaries with various component
masses was followed until the primary component reached the critical Roche
surface and the Roche lobe overflow (RLOF) began. It was assumed that the
minimum initial, i.e. ZAMS, orbital period of such binaries is equal to 2 d and
that the components lose AM just as single stars. According to the
mass-dependent formula for AM loss rate of single stars, derived in this paper,
the AM loss time scale increases substantially with decreasing stellar mass.
The formula was applied to binaries with the initial primary component masses
between 1.0 and 0.6 solar mass and two values of mass ratio q=1 and 0.5.
  Detailed calculations show that the time needed to reach RLOF by a 1 solar
mass primary is of the order of 7.5 Gyr, but it increases to more than 13 Gyr
for a binary with an initial primary mass of 0.7 solar mass. Binaries with less
massive primaries have not yet had time to reach RLOF even within the age of
the Universe. This sets a lower mass limit for the presently existing contact
binaries
