Radius Vectors & Velocity V - Exploring the Angle

[captain]

what do radius vectors of particles really mean and how can they be at a different angle with velocity v.

 

[bsmith2000]

The radius vector $$\vec{r}$$ is the vector from some origin to the position of the particle at some time $$t$$. Typically, $$\vec{r}(t)$$ is the trajectory, so to speak of the particle, so the derivative with respect to time is the velocity: $$v_t = \frac{d\vec{r}}{dt}$$. Because the position is constantly changing, the velocity as well as the angle changes with respect to the origin.

Does that answer your question?

 

[Loren Booda]

Consider yourself at the origin of a coordinate system. Any vector connecting you with an object is radial. That object may change its position, shown by a velocity vector, which is often not along the radial vector.

For instance, although motion along a circle is confined to a given radial distance out from the center, velocity is restricted to move tangent to the circle, and the acceleration enforcing circular motion orients radially toward the center!