Spec Rel: Changes in gradient between frames

[Totoro Recall]

Homework Statement

Suppose a rod measured in the S frame has a gradient of M.

The S' frame travels at v (along x-axis) relative to S. What is the gradient of the rod in the S' frame?

Homework Equations

Lorentz tranformations

The Attempt at a Solution

y'=y


x' = $\gamma$(x-vt)


so that m = y'/$\gamma$(x-vt)


This seems straightforward enough, which is why I'm worried. I'm not used to problems in relativity being this easy. Have I missed anything?

 

[anathema]

I can confirm that your solution is correct. The Lorentz transformations allow us to calculate the measurements of an object in one frame of reference from measurements in another frame of reference. In this case, the gradient of the rod in the S' frame would be the same as in the S frame, as the length of the rod would not change due to its orientation being perpendicular to the direction of motion. This is a fundamental concept in relativity and is a key part of understanding the effects of time and space in different frames of reference. Keep up the good work!