Pedagogical Training: Mechanics of Point Particles on Curved Surfaces

This lecture covers the physics of a point particle sliding without friction on a curved surface, focusing on writing and analyzing the differential equations of motion, determining the reference frame, constraints, kinematics, forces, and dynamics involved. The lecture also delves into the absolute acceleration vector, external forces like weight and normal reaction force, and the application of Newton's second law to derive scalar equations of motion in spherical coordinates. The dynamics of the point particle are thoroughly explained, considering the forces and accelerations in spherical coordinates. The lecture concludes by simplifying the motion description to polar coordinates in a vertical plane, illustrating the mechanics of a point particle sliding on a rotating disk.