If we have a stable system of particles that were, lets say, orbiting a common center at angular speed w, and we gave the system a linear velocity v, how would we properly add the two velocities? Now lets assume these particles are light speed particles. Any given observer will therefore measure their total velocity as constant. Would this make it a simple vector addition?

total v =w+v =c

If that’s right then we can write

total v=sqr(v^2 + w^2)

Or is all of this wrong? :confused:

Natural:

<i>If we have a stable system of particles that were, lets say, orbiting a common center at angular speed w, and we gave the system a linear velocity v, how would we properly add the two velocities?</i>

First, let me say I don't think you mean angular speed here. If you do actually mean that, then the addition can't be done, because angular speed is measured in radians per second, whilst linear speed is in metres per second. The units are incompatible.

To add two linear speeds in relativity, you need to use the relativistic velocity addition formula.

And there are no light speed particles (except for massless particles such as photons).

James:
First, let me say I don't think you mean angular speed here.

You're right, I should have said angular velocity.

To add two linear speeds in relativity, you need to use the relativistic velocity addition formula.

I'm not asking about two linear speeds, I'm asking about adding a rotational velocity and a linear velocity.

And there are no light speed particles (except for massless particles such as photons).

Or maybe neutrinoes. But really, this system is a valid concept to inquire about, after all, someday some genius might discover a model of the structure of a massive particle that works really well. Whatever building blocks it uses, like quarks, I'd bet they will differ from known particles today. If your point is that there exists no system of photons that orbit a common center, well, I'm aware of that. When inquiring in new directions, new concepts are sometimes in order.

Natural:

You can't add something with dimensions of time^-1 (e.g. angular velocity) to something with dimensions length.time^-1 (e.g. linear velocity). If you want to add these two things, you need to convert one of them into the other.

The relationship between angular velocity <b>w</b> and the corresponding linear velocity <b>v</b> is

<b>v</b> = <b>w</b> &times; <b>r</b>,

where <b>r</b> is the displacement vector which points from the rotational axis to the point whose linear velocity you are trying to determine.

If you first convert an angular velocity to a linear velocity, then you can add it to another linear velocity using the usual relativistic velocity addition formula.