# Velocity addition

1. Oct 31, 2009

### E92M3

I know how to add speed in special relativity.

$$v=\frac{u+v'}{1-\frac{uv'}{c^2}}$$

Is this a vector thus velocity? Or does this only apply to objects traveling on the same axis? Judging from the way it's derived, I really think that it only applies to objects on the same axis. What if I want to look at say...an object going north and an object going east in the rest frame. What then is their velocity in the frame of one of the objects?

2. Oct 31, 2009

### Vanadium 50

Staff Emeritus
It's only for motion along one axis. You can check this yourself: if you consider the non-relativistic limit, you only get the right answer for motion along one axis.

3. Oct 31, 2009

### Staff: Mentor

As you realize, the formula you quoted (once you correct the sign error in the denominator) is only for the special case of parallel velocities. Read about the more general case here: http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html" [Broken]

Last edited by a moderator: May 4, 2017
4. Oct 31, 2009

### clem

You should have a plus sign in the denominator.
There is a different formula for u and v perpendicular.

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