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Shamelessly ripping from Tom Moore's answer to the same question some years back (https://answers.ros.org/question/192273/how-to-implement-velocity-transformation/).

To add on more concisely, a velocity vector is just a vector like any other quantity. You can transform vectors from one frame to another through some simple matrix multiplication that TF (TF2) will take care of for you.

See TF2 docs for specifics http://docs.ros.org/melodic/api/tf2/html/