Fixed and Moving Reference Frames for adding speeds

AI Thread Summary
Adding velocities from different coordinate systems involves understanding the relative motion of objects, such as a planet gear rotating both on its axis and around its carrier. The velocity of the planet gear relative to the carrier is calculated by subtracting the carrier's velocity from the planet's local velocity. There is no mathematical proof for this addition of velocities; it is derived empirically and serves as an approximation for small relative velocities. For higher speeds, the Lorentz transformation should be used instead of the Galilean transformation. Understanding these concepts is crucial for accurately analyzing motion in different reference frames.
bugatti79
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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?
 
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