Objectives
This unit covers the following ideas.
Develop formulas for the velocity and position of a projectile, if we neglect air resistance and consider only acceleration due to gravity. Show how to find the range, maximum height, and flight time of the projectile.
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Develop the \(TNB\) frame for describing motion. Explain why \(\vec T\text{,}\) \(\vec N\text{,}\) and \(\vec B\) are all orthogonal unit vectors, and how to perform the computations to find these three vectors.
Compute the unit tangent and unit normal vector of space curves
Explain the concepts of curvature \(\kappa\text{,}\) radius of curvature \(\rho\text{,}\) center of curvature, and torsion \(\tau\text{.}\) Including what these quantities mean geometrically.
Find the tangential and normal components of acceleration. Show how to obtain the formulas \(a_T=\frac{d}{dt}|\vec v|\) and \(a_N=\kappa |\vec v|^2=\frac{|\vec v|^2}{\rho}\text{,}\) and explain what these equations physically imply.