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Leo Liu
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This derivation is found in Kleppner's mechanics book. It shows how to find the acceleration in rotating coordinates by differentiating ##\vec v_{in}=\vec v_{rot}+\vec\Omega\times\vec r##; subscripts IN and ROT stand for inertial and rotation respectively.
My question is what the term ##\left(\frac{d\vec v_{in}}{dt}\right)_{rot}## means. Is it the same thing as ##\frac{d\vec v_{rot}}{dt}##? Thank you.
Edit 1: It appears that someone has asked a similar question 12 years ago.
https://www.physicsforums.com/threads/deriving-acceleration-in-rotating-reference-frames.286812/
Edit 2: Meh, it was of no help ¯\_(ツ)_/¯ .
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