Hidden momentum of composite bodies and magnetic dipoles

Hidden momentum is a puzzling phenomenon associated with magnetic dipoles and other extended relativistic systems. We point out that the origin of hidden momentum lies in the effective change of individual particle masses of a composite body, during which the total momentum of the system is not equal to the momentum of the center of mass. Defining the hidden momentum as the difference between the total momentum and the center-of-mass momentum, we explain in detail how hidden momentum arises in certain simple non-relativistic systems, in typical relativistic systems due to velocity-dependent ``relativistic mass'', and in magnetic dipoles as a special case of relativistic systems.