This paper introduces a task-space dynamics formulation for fixed-base serial-link kinematically redundant manipulators and a motion/force controller based on it. The aim is to alleviate joint-space instability problems that have been observed with other motion/force controllers. The dynamics are represented in floating-base coordinates, wherein the end effector is regarded as the floating base. This representation gives rise to a momentum-conserving redundancy resolution scheme based on the reaction null-space (RNS) method used in past studies on free-floating and flexible-base space robots. A generalized inverse is obtained that is shown to satisfy the conditions for dynamic consistency in the sense of the operational space (OS) formulation, but may lead to the joint-space instabilities observed earlier. The proposed controller is based on the pseudoinverse of the coupling inertia matrix and ensures reactionless link motion that does not disturb the force balance at the end effector. The performance of the RNS motion/force controller is examined by comparison to that with an OS motion/force controller. It is shown that while the performance in task-space of both controllers is satisfactory, the joint-space performance of the proposed controller is superior.