Relation between position vector and velocity vector

[Happiness]

The equation following (3.80) seems to suggest that the velocity vector ##\vec{\dot{r}}## must always be parallel to the position vector ##\vec{r}##. But clearly this is not true as a particle's velocity can be in any direction.

What's wrong?

 

[PeroK]

That looks like the acceleration vector for a central force, which must indeed be in the direction of the position vector (from the central point).

The last equation says "the component of the velocity in the radial direction". There is an angular component as well.

 

[Happiness]

That looks like the acceleration vector for a central force, which must indeed be in the direction of the position vector (from the central point).

The last equation says "the component of the velocity in the radial direction". There is an angular component as well.

##\vec{\dot{r}}##should be the velocity vector. The acceleration vector should be ##\vec{\ddot{r}}##.

I think I get it. ##\dot{r}\neq|\vec{\dot{r}}|##.