# Is radial velocity parallel to radius of curvature or the position vector?

I'm a bit confused regarding the directions of velocities and acceleration in curvilinear motion. Assume a curvilinear motion, which is not circular. I know that tangential component of velocity and acceleration are tangential to the curve at any point on the curve. But what about normal acceleration and normal velocity?

2. Are they in the same direction of the position vector r?
3. Or are they parallel to radius of curvature of the curve?
• What is the definition of a tangent to a curve described by the position vector $\vec r(\alpha)$ at one point (characterized by the parameter $\alpha =\alpha_0$? the limit of $\frac{{\vec r}(\alpha_0 + \Delta \alpha )-{\vec r}(\alpha_0)}{\Delta \alpha}$ for $\Delta \alpha \rightarrow 0$. A part of the choice of the parameterization, where does it differ from the definition of velocity? Dec 2 '20 at 18:37