# Frame of reference

1. Jun 17, 2006

### whoelsebutme

Frame of reference....

Ok here's a question inspired by relativity and frames of reference.

In a funfair, there are two carousels (merry-go-rounds), each 4 meters in diameter and their centers 5 meters apart. They revolve with the same angular velocity, but in opposite directions. We have two twins P and Q on these carousels. Going round the carousels they pass each other several times.

Later, when they are sitting down and enjoying their meals, P tells Q that her carousel was faster because she always seemed to overtake Q. Q said he also felt exactly the same thing - that his carousel was faster!

What's happening?! Why does each one feel that he/she is faster than the other?

2. Jun 17, 2006

### rcgldr

I don't understand, if the two carousels have the same angular velocity then no one is passing anyone. If P and Q start off next to each other, then they will always "meet" up at the same place. It's similar to pairs in ice skating where they sink up their orientation as well as rotational speed.

Last edited: Jun 17, 2006
3. Jun 17, 2006

### Danger

If this was a real-life event, rather than a thought experiment, then there might have been an optical illusion based upon each person's perception of the angular velocity constantly changing. That's just a guess, though.

4. Jun 20, 2006

### actionintegral

I think your guess is right , Danger, if they are out of phase. A would see B approach the osculating point faster, and then, after leaving maybe B would appear to slow down or something

5. Jun 22, 2006

### jasc15

even if they were out of phase, the amount by which they were out of phase would remain constant the whole time

6. Jun 22, 2006

### Danger

True, but that's not quite what I meant. My reference was to the fact that each person's angular velocity relative to the other person is constantly changing. First they head straight toward each other, then travel side-by-side, then head apart.