Oscillations of superconducting current between clockwis e and counterclockwise directions in a flux qubit do not conserve the angular momentum of the qubit. T o compensate for this effect the solid containing the qubit must oscillate in unison with the current. This requires entanglement of quantum states of the qubit with quantum states of a macrosco pic body. The question then arises whether slow decoherence of quantum oscillations of the cur rent is consistent with fast decoherence of quantum states of a macroscopic solid. This problem is ana lyzed within an exactly solvable quantum model of a qubit embedded in an absolutely rigid soli d and for the elastic model that conserves the total angular momentum. We show that while the quantum state of a flux qubit is, in general, a mixture of a large number of rotational stat es, slow decoherence is permitted if the system is macroscopically large. Practical implicatio ns of entanglement of qubit states with mechanical rotations are discussed.