  We make a semi-classical steady state analysis of the influence of mirror
motion on the quantum phase transition for an optomechanical Dicke model in the
thermodynamic limit. An additional external mechanical pump is shown to modify
the critical value of atom-photon coupling needed to observe the quantum phase
transition. We further show how to choose the mechanical pump frequency and
cavity-laser detuning to produce extremely cold condensates. The present system
can be used as a quantum device to measure weak forces.
