(Lecture: 30 minutes)
This lecture consists largely of a mathematical derivation of the modified second law, and the identification of the Coriolis and centrifugal accelerations. How much detail to present will depend on the students' (and instructor's) comfort with this style of derivation.
Some of the students may have seen a special case of this computation when studying orbital mechanics in the Central Forces Paradigms.
One possible path through this material is to start directly with the difference between “naive” and “true” time derivatives, emphasizing the cross product with the angular velocity from the beginning. The derivative formulas for the rotating basis vectors can even be quoted without proof, referring students to the lecture notes for the derivation. The instructor will need to balance a desire to provide a self-contained presentation with the difficulty of engaging the students in the detailed derivation.
The instructor should take care to adequately motivate the mathematical derivation.