# 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?
• Thanks, I read that one. I think I'm clear on the acceleration front now. If I'm right, acceleration has a tangential component, and a normal/centripetal component which is parallel to the radius of curvature at any point in the curve. But what about radial and normal velocity? Are they parallel to the radius of curvature or the position vector, given that radial velocity is dr/dt? Dec 2 '20 at 18:19
• By definition, there is no component of the velocity but the tangential one. Dec 2 '20 at 18:23
• No, that's only when radial velocity (dr/dt) is zero. Like in uniform circular motion. Otherwise there can be a radial velocity component. Dec 2 '20 at 18:26
• 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 