Abstract: Applied mechanics courses are key foundation of modern engineering education. As the starting point, “classical mechanics” provides fundamental concepts and principles for all other branches of applied mechanics. On one hand, there exist both close connections and evident differences between “classical mechanics” (discrete systems) and continuum mechanics (continuum systems). On the other hand, dynamical system theory and nonlinear science, both originated in classical mechanics, have notable effects on all applied mechanics branches. By focusing on these two aspects, connections will be detailed in a series of papers titled “A new research-oriented lecturing methodology of classical mechanics” by the authors, with the current one devoted to velocity formula of rigid body motion and decomposition of continuum velocity field, which are key kinematic results for rigid body mechanics and continuum mechanics, respectively. The former is built on the concept of angular velocity of rigid body while the latter is characterized by the gradient tensor of velocity field. This paper will demonstrate that, the two formulae, seemingly different, essentially correspond to each other. Explicitly, the rigid body formula is the degenerate case of the general velocity field decomposition, by neglecting deformation effects.