Normal and Tangential Acceleration

This lecture revisits the concept of vector acceleration, linking changes in velocity to forces acting on a point. It introduces the notion of curvilinear abscissa to understand that velocity is tangential to the trajectory, while acceleration has both tangential and normal components. The instructor defines curvilinear abscissa, scalar velocity, and vector velocity in terms of the abscissa. The lecture explores the physical meaning of the derivative dr/ds, showing that it is tangent to the trajectory and has a unit length. It then delves into vector acceleration, decomposing it into tangential and normal components, related to changes in scalar velocity and the curvature of the trajectory. The analysis concludes by explaining the two terms of vector acceleration, one related to the derivative of scalar velocity and the other to v²/r, where r is the radius of curvature.