Knowing accurately the dynamic parameters of a manipulated object is required for common coordination strategies in physical human-robot interaction. Bias in object dynamics results in inaccurately calculated robot wrenches, which may disturb the human during interaction and bias the recognition of the human motion intention. This paper presents an identification strategy of object dynamics for physical human-robot interaction, which allows the tracking of desired human motion and inducing the motions necessary for parameter identification. The estimation of object dynamics is performed online and the estimator minimizes the least square error between the measured and estimated wrenches acting on the object. Identification-relevant motions are derived by analyzing the persistence of excitation condition, necessary for estimation convergence. Such motions are projected in the null space of the partial grasp matrix, relating the human and the robot redundant motion directions, to avoid disturbance of the human desired motion. The approach is evaluated in a physical human-robot object manipulation scenario.