Acceleration Tensor - Rotating Frame

1. Feb 13, 2006

PrinceOfDarkness

If a coordinate system is rotating, that is time 't' is not independent, then does the acceleration transform as rank 1 tensor?

I thought that it wouldn't because when time is changing, so acceleration will change in a more complicated way than a rank 1 tensor. Perhaps as a rank 2 tensor.

This Q is really troubling me. There are two groups in my class, one saying it still transforms as a rank 1 tensor, the other saying it doesn't transform as a rank 1 tensor. Some even say that acceleration never transforms like a rank 1 tensor. I wonder how! I think it transforms like a rank 1 tensor if it goes fixed rotation, but 'rotating' coordinate system will mean that transformation is more complicated.

2. Feb 16, 2006

dextercioby

Rotations (with presumably fixed angular velocity) are examples of (restricted) Lorentz transformations. If you know how the acceleration behaves when being subject to a (restricted) Lorentz transformation, then everything would be fine, wouldn't you say...?

Daniel.

3. Mar 5, 2006

pervect

Staff Emeritus
You need to be a bit more specific here. The 4-acceleration is a geometric object, so it transforms as a tensor.

A rotating coordinate system will require a metric that is not Minkowskian, so you start getting into GR rather than SR.

The rotating coordinate system will be ill-behaved when r*w = c, some of the metric coefficients go to zero (or was it infinity? I'd have to double check - but I know they are not well-behaved).

4. Mar 5, 2006

Hurkyl

Staff Emeritus
No, you're merely getting into differential geometry.