Thank you for the opportunity to help you with your question!

The radius of curvature is given by

r=1/k

where is the curvature.
At a given point on a curve, is the radius of
the osculating circle. The symbol is sometimes
used instead of to denote the radius of curvature

Let and be given parametrically
by

x=x(t)

y=y(t)

then,

R=[1+(dy/dx)^2]^3/2 /Id^2y/dx^2I

acceleration=v(d,theta/ dt)

a=vw

a=rw^2

a=v^2/r

Please let me know if you need any clarification. I'm always happy to answer your questions.