Position Vector: Why Does it Always Point Radially Outward?

[Swapnil]

I was wondering, why does the position vector always points radially out from the center (for example, in circular motion). I figure that this is because $$\vec{v} = \frac{d \vec{r}}{dt}$$ and the velocity should always be tangent to the "curve" (because of Newton's first law).

But is there any other reason to make the position vector point radially outward??

 

[daveb]

It only points radially outward because you choose your origin at a specific point. I could just as easily decide the origin is on some pint of the circular pathway, though the math would be a tad more difficult.

 

[Cyrus]

I was wondering, why does the position vector always points radially out from the center (for example, in circular motion). I figure that this is because $$\vec{v} = \frac{d \vec{r}}{dt}$$ and the velocity should always be tangent to the "curve" (because of Newton's first law).

But is there any other reason to make the position vector point radially outward??

Well, that is why its called the radial position.

You have three components. One is radial, one is tangent, and one is normal to the two of those. We use them becuase they are useful in curvilinear motion. If we used x,y,z vectors, we would have components in all 3 directions. Using radial coordinates we do not have to find components along the directions we care about. It just makes life easier. And, as you will find later in life, it is essential in fluid dynamics for the bernoulli equation.