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

Question

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?

Are they same as radial acceleration and radial velocity?
Are they in the same direction of the position vector r?
Or are they parallel to radius of curvature of the curve?

Aseem Mittal · Answer

I don't think there is anything like normal velocity. Velocity acts only along the direction tangential to the path of the object.
To prove my point lets say that there is a component of velocity in direction not tangential to the path. Then after moving over a differential element we would end up at a point in the direction of the net velocity which would deviate from its original path.

As for the normal acceleration, it is along the radius of curvature and is responsible for rotating the velocity vector and turning the direction of motion along the path

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

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