Questions regarding relativistic momentum

[nos]

Hi everyone,

I found a derivation for relativistic momentum on this page:
http://en.wikibooks.org/wiki/Special_Relativity/Dynamics

I understand it all the way through, except the point where they have come to this equation.

m$_{red} =$$\frac{m_{blue}}{\sqrt{1-(\frac{u(x,r)}{c})^{2}}}$

Where(as I understand correctly) m_blue is the mass according to the frame moving at the same x-velocity as the blue ball and where m_red is the mass of the red ball according to the frame moving with the same x-velocity as the blue ball.

Then they go to:

M =$\frac{m_{0}}{\sqrt{1-(\frac{u}{c})^{2}}}$

Where u is now the relative velocity of the red ball for the moving frame.
But that is what I don't understand. How can they suddenly ignore the relativistic effects of the y-velocities? The first equation gives the mass of red ball in terms of the relative x-velocity of the red ball. Then how do they get to relativistic mass in terms of the relative velocity u? Because u_x,red is only the x component velocity and u_red has both a x-component and y-component.

This is my hypothesis:

They let both u_y,red and u_{y, blue} approach zero. So that the mass of the blue ball will correspond to the rest mass and that the relativistic effects of the y-velocities will cancel.

Thank you.

 

[Dale]

Wow, that is a really complicated derivation of relativistic momentum. I would recommend simply learning four-vectors:
http://en.wikipedia.org/wiki/Four-vector
http://en.wikipedia.org/wiki/Four-momentum

It seems easier, and will definitely be much more generally useful.