Answer to Question #315371 in Mechanics | Relativity for Aune

Question

Find the unit tangent vector, the unit normal vector, the curvature and the radius of curvature of the circle x= a cos theta, y= a sin theta, z=0 at point with parameter theta.

Answer 1

Answer

According to concepts

N(t)=T′(t)||T′(t)||. Comparing this with the formula for the unit tangent vector, if we think of the unit tangent vector as a vector valued function, then the principal unit normal vector is the unit tangent vector of the unit tangent vector function.