Radius of Curvature Proof - approximating a curve with a circle!

The video tutorial explains the concept of radius of curvature, illustrating how a particle's path can be modeled as a circular path at any instant. It details the calculation of the radius of curvature using circular motion formulas, specifically focusing on deriving DS and D Theta. The tutorial further explains the differentiation process to find D Theta and derives the final formula for the radius of curvature. The video concludes with a simplification of the formula and a discussion on the use of absolute value to ensure a positive radius of curvature.

What is the relationship between tan Theta and the slope DY/DX?

How do we differentiate tan Theta with respect to X?

Why is the radius of curvature sometimes written with an absolute value sign?