Fictitious forces in rotating frames of reference

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SUMMARY

The discussion centers on the derivation of fictitious forces in rotating frames of reference, specifically referencing the transport theorem as applied to vector quantities. The user expresses confusion regarding the application of the theorem to velocity vectors, leading to the equation F = F' + w × v. A critical error is identified: the user neglects to account for the mass of the particle, which is essential for correctly relating acceleration to force through Newton's second law.

PREREQUISITES
  • Understanding of fictitious forces in physics
  • Familiarity with the transport theorem in vector calculus
  • Knowledge of Newton's laws of motion
  • Basic concepts of rotating frames of reference
NEXT STEPS
  • Study the transport theorem in detail, focusing on its application to vector fields
  • Review Newton's second law and its implications in non-inertial frames
  • Explore examples of fictitious forces, such as the Coriolis and centrifugal forces
  • Examine the mathematical derivation of forces in rotating frames using specific case studies
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in the dynamics of rotating systems will benefit from this discussion.

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I got stuck going over the derivation of fictitious forces in rotating frames.
see specifically
http://en.wikipedia.org/wiki/Rotating_reference_frame#Time_derivatives_in_the_two_frames
this page to see the proof I'm talking about
(sorry i'd love to be able to explain it by myself but wikipedia page is so much clearer)
the part I'm stuck on is the use of the transport theorem, it's supposed to work on any vectors right?
so let Q be any vector
then
dQ/dt = dQ'/dt + w×Q
so what if i let Q = v, the velocity of the particle, doesn't this directly giv
F =F' + w×v

PLEASE SOMEONE TELL ME WHAT I DID WRONG!
 
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you forgot about the mass of the particle. dv/dt is the acceleration, not the force
 

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