Position Vector: Why Does it Always Point Radially Outward?

In summary, the position vector always points radially out from the center in circular motion because it is defined as the radial position. This makes it easier to deal with the components in curvilinear motion and is essential in fluid dynamics for the bernoulli equation.
  • #1
Swapnil
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6
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 [tex]\vec{v} = \frac{d \vec{r}}{dt}[/tex] 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??
 
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  • #2
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.
 
  • #3
Swapnil said:
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 [tex]\vec{v} = \frac{d \vec{r}}{dt}[/tex] 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. :wink:

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.
 

1. What is a position vector?

A position vector is a mathematical concept used to describe the position of a point in space. It is represented by an arrow pointing from the origin to the point, with its length representing the distance and its direction representing the direction of the point from the origin.

2. Why does a position vector always point radially outward?

A position vector always points radially outward because it is defined as the vector connecting the origin to a point. This means that its direction is always away from the origin and towards the point, resulting in a radial outward direction.

3. Is the position vector the same as the displacement vector?

No, the position vector and the displacement vector are not the same. The position vector describes the location of a point in space, while the displacement vector describes the change in position of a point from one location to another.

4. How is a position vector calculated?

A position vector can be calculated using the coordinates of a point in space. The vector is formed by subtracting the coordinates of the origin from the coordinates of the point, resulting in a vector with its tail at the origin and its head at the point.

5. Can a position vector have a negative direction?

Yes, a position vector can have a negative direction. This indicates that the point is located in the opposite direction from the origin. However, the magnitude of the vector (its length) is always positive, as it represents the distance between the point and the origin.

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