Fixed and Moving Reference Frames for adding speeds

[bugatti79]

Hi Folks,

I have some misunderstanding how one can add velocities of different coordinate systems.

Consider a planet gear rotating about its own axis and also rotating on its carrier so that the so called velocity of the planet gear relative to the carrier is the planet local velocity minus the carrier velocity.

How can one add to different velocities that are at different points in space?
is there a mathematical proof?

 

[A.T.]

See:
http://en.wikipedia.org/wiki/Galilean_transformation

Hi Folks, is there a mathematical proof?

No, it's was derived empirically, and is just an approximation valid for small relative velocities. Otherwise you have to use:
http://en.wikipedia.org/wiki/Lorentz_transformation