We perform a detailed quantum study of forced molecular rotation in an optical centrifuge, recently proposed by J. Karczmarek [Phys, Rev. Lett. 82, 3420 (1999)]. The approach uses strong nonresonant laser fields with chirped frequency to induce efficient rotational excitation of anisotropic molecules via a sequence of Raman transitions. Quantum calculations firstly of angular confinement (angular trapping) of a molecule in the early stages of the centrifuge evolution and secondly of the resulting rotational dissociation process are carried out herein. The trapping calculations include both angular degrees of freedom while the dissociation calculations include one vibrational and one rotation degree of freedom. Diatomic Cl-2 is used as a test case. An extension of the scheme outlined by Karczmarek is proposed as a method of producing molecules in a single selected J = J(z) level. (C) 2001 American Institute of Physics.