Calculus Animations,Graphics and Lecture Notes Unit Tangent Vectors/Unit Normal Vectors
 Home About Kelly Liakos Sponsors Calculus 1- Limits and Derivatives Calculus 1 - The Second Derivative Calculus 1 and 3 Formula Sheets Chain Rule Computer Lab Assignments Conic Sections Differential Equations Directional Derivatives/Gradient Double Integrals Equillibrium Solutions 1st order DEs 1st order Diff Eqs -Motion Flux Integrals and Surface Integrals Infinite Sequences Infinie Series Level Curves and Level Surfaces Line Integrals Optimization and Related Rates Optimization for Functions of 2 Variables Parametric Equations 2-space Parametric Equations 3-space Partial Derivatives Polar Coordinate System Polar Coordinates- Derivatives and Integrals PreCalculus Riemann Sums and the Fundamental Theorem of Calculus 2d order Diff EQS-Motion 2d Partial Derivatives Supplemental Exercises and Solutions Tangent Planes/ Differential for f(x,y) Trigonometry Trigonometry Applications Triple Integrals Unit Tangent Vectors/Unit Normal Vectors Vectors in General Vector Valued Functions Visualizing Limits of Functions of 2 Variables Work Links Special Topics Scratch Paper 2 Poems

A particle can acclerate in 2 ways, either a change in direction or a change in speed.

The purpose of this discussion is to formulate velocity and acceleration of a particle at a point in terms of vectors tangent and perpendicular to the trajectory at this point.

It is broken into 4 parts:

1. A discussion of  the unit tangent and unit normal vectors

2. Arclength parameterization

3. Curvature

4. Formulating the acceleration in components aT and aN - the tangential anf normal components .

 Notes - Unit Tangents and Unit Normals Animation 1 Animation 2 The following are the notes and animations for a 3D example of unit tangents and unit normalsfor a helix. Notes - Unit Tangent and Unit Normal for a Helix Animation 1 Animation 2 Notes- Arclength Parameterrization Animation 1 Animation 2 Notes- Curvature Notes- Tangential and Normal Components of acceleration

The Smart Bunny-A very short story by Kurt Vonnegut Jr.