Expression for the centripetal acceleration

Is the expression $$\frac{v^2}{r}$$ for centripetal acceleration,only valid for uniform circular motion, or is it also valid even when particle is moving in a non-uniform circular motion?

• It applies to any smooth path. And the specific case of non-uniform circular motion is explicitly discussed here. – lemon Jan 12 '18 at 10:34

where $s$ is the arclength, $\kappa$ is the curvature and $\rho$ is the radius of curvature.
Acceleration will include the tangential component (along $\mathbf{T}$) and normal component (along $\mathbf{N}$) which is the centripetal acceleration but is given by radius of curvature instead.