# Simple difference between module of velocity and time derivative of module of position [duplicate]

What is the conceptually difference between the two: $$\frac{d|\vec{r}|}{dt}=\frac{\vec{r}\cdot\frac{d\vec{r}}{dt}}{|\vec{r}|}\neq|\dot{\vec{r}}|\equiv \bigg|\frac{d\vec{r}}{dt}\bigg|$$ Unidimensionally it appears an equality, but Im having trouble to think qualitatively.

• Does $|\dot{\vec{r}}|$ mean the absolute value of velocity, i.e. $|\frac{d\vec{r}}{dt}|$? Jun 3 at 16:35

These two quantities are clearly different. For an object moving at constant speed $$v$$ in a circle, the former is zero, whereas the latter is exactly $$v$$.