# What happens to objects along spiral galaxy arms over long periods of time?

Observations of spiral galaxies reveal that objects within the same arm of a spiral galaxy move at around the same speeds, regardless of their distance from the center of the galaxy. Conversely, the speed of points on a fan blade vary with their distance from the center, such that the outside of the blade is rotating faster than the inside of the blade. This would be required for the blades of a fan to remain rigid and extending along a radius of the fan.

I imagine the curved shape of spiral galaxy arms is due to the points along the arm remaining at the same speed. However, I am curious what this phenomenon does to the shape of spiral galaxies and objects within them over long periods of time.

Let's take two arms of a hypothetical spiral galaxy, and two points within each arm. The arms extend straight along a radius from the center at 0° and 270°. The galaxy is rotating clockwise. The closest two points in arms 1 and 2 are ~0.159 from the center of the galaxy where they rotate along a circumference of 1 , at a velocity of 0.25. The outer two points in arms 1 and 2 are ~0.318 from the center of the galaxy, where they rotate along a circumference of 2, at a velocity of 0.25:

The table below describes their positions at time-steps 0 to 4:

At the end of time-step 4, points 1 and 3 have gone through one full rotation, while points 2 and 4 will have gone through one half of a rotation. This means that points that originally started along the same radius (within the same arm) are now at the opposing ends of the galaxy.

How does this play out in our current models galaxy dynamics? Do spiral arms eventually dissipate? Do objects at the outer edge of spiral arms fall into the arms adjacent to them?