Normal and Tangential Coordinate Systems | Axes Aligned with a Path | Centripetal Acceleration

LECTURE 02a Here the normal-tangential (n-t) coordinate system is described and the associated kinematic vector equation is derived for acceleration. Since this type of coordinate system will inherently rotate due to tracking along curvy paths, it becomes necessary to derive and describe the meaning of the time derivative of the tangential unit vector. The resulting equation includes a term that is radius of curvature of the path, thus the mathematical relationship describing radius of curvature in terms of the derivatives of a spatial function are reviewed. An example is demonstrated in which an object is moving along a path described by a spatial function at a speed given by a function in terms of time. The acceleration vector of the object is determined at a particular time and spatial location. The video segment concludes with a discussion of the types of acceleration (i.e. along the path vs. transverse to the path) in the context of what a passenger feels when riding in an automobile. Playlist for MEEN203 (Dynamics):    • MEMT 203: Dynamics   This lecture segment was recorded on June 5, 2018. All retainable rights are claimed by Michael Swanbom. Please subscribe to my YouTube channel and follow me on Twitter: @TheBom_PE Thank you for your support!