Why are rectangular unit vectors constant while polar unit vectors change?

[delve]

Why are rectangular unit vectors constant in time whereas those of a polar coordinate or spherical coordinate system aren't?

 

[rochfor1]

How is anything changing in time? You need to be waaaay more specific.

 

[delve]

Could you help me figure out how I can be more specific?

 

[arildno]

Why are rectangular unit vectors constant in time whereas those of a polar coordinate or spherical coordinate system aren't?

THe unit vector in the x-direction is orthogonal to the surface x=some constant (i.e, planes).

Thus, all these unit vectors in the x-direction are PARALLELL to each other, and thus, essentially, the same vector.

The radial vector, however, is orthogonal to the surface r=some constant (i.e, spheres)

Along each such surface, non-paralllell radial vectors abound, and thus, the unit radial vactor is NOT the same at different points on the surface.

 

[delve]

I believe that makes sense, thank you!