Quick question on vectors in polar coordinates

[schlynn]

This is more of a general question, really no math involved. Since polar coordinates are, (theta, r), the direction of the vector is theta, and the magnitude is r, in polar coordinates, does a vector represent rotational force?

 

[fatra2]

Hi there,

No necessiraly. Different coordinates will be used to solve different problems. But every coordinate can be used to solve every problem.

Let me explain a bit more, it might get clearer. You and I know that some equations in the square coor (x,y,z) become very complicated, specially in cases where the vector is not linear, but following some curvature. Therefore, the polar coor will be preferred in cases where it simplifies the math.

To give you a simple example, take a vector of radius r=1, which remains fix. The vector direction varies over time. Therefore, if you would have to write equation in (x,y,z) to explain it's behaviour in time, you would have (x,y,z) that varies all the time. Which in a polar coor you only have $$\theta$$ that varies.

Hope this makes it clear enough? Cheers

 

[HallsofIvy]

This is more of a general question, really no math involved. Since polar coordinates are, (theta, r), the direction of the vector is theta, and the magnitude is r, in polar coordinates, does a vector represent rotational force?

It is actually most common t represent vectors, even in polar coordinates, with x and y components, but yes, you can have "radial" and "angular" components. Writing vectors as $\left< r, \theta\right>$, a vector with 0 radial component would represent a "rotation". Of course, vectors don't necessarily represent forces.