In quantum mechanics, students learn that angular momentum has two parts: intrinsic (or spin), and wave (or orbital) contributions. This separation is analogous to the separation of momentum into two parts when analyzing waves: intrinsic momentum associated with motion of the inertial medium, and wave momentum associated with propagation of energy by the wave. However, spin angular momentum can seem mysterious to students because, unlike the moment of momentum, it is independent of any coordinate origin. This difficulty can be overcome by teaching students the coordinate-independent definition of angular momentum density: the vector field whose curl is equal to twice the intrinsic momentum density. This definition of intrinsic angular momentum density, or spin density, is applicable in both classical and quantum physics. This paper gives specific examples illustrating how spin density describes the angular momentum of rigidly rotating objects. The relationships between spin density, velocity, and angular velocity are similar to the relationships between vector potential, magnetic field, and electric current in magnetostatics. Appreciation of the coordinate-independent description of angular momentum will remove one obstacle to students' understanding of quantum mechanics.