- #1

Mr.Miyagi

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In my mechanics book a derivation is given for acceleration in rotating reference frames. However, there is one step I don't understand.

First of all, it is derived that [tex]v=v'+\omega\times r'[/tex] or [tex]\left( \frac{dr}{dt}\right) _{fixed}=\left( \frac{dr'}{dt}\right) _{rot}+\omega\times r'[/tex]

The unprimed vectors are relative to the fixed reference frame and the primed vectors to the rotating one. Then it is claimed that this should hold for any vector:

[tex]\left( \frac{dQ}{dt}\right) _{fixed}=\left( \frac{dQ}{dt}\right) _{rot}+\omega\times Q[/tex]

In particular, it holds for the velocity vector:

[tex]\left( \frac{dv}{dt}\right) _{fixed}=\left( \frac{dv}{dt}\right) _{rot}+\omega\times v[/tex]

In this equation v can be substituted as [tex]v=v'+\omega\times r'[/tex] and then, after some algebraic manipulation, one can find the fictitious forces.

What i don't understand is why the primes are suddenly being dropped. Why are vectors relative to the rotating reference frame suddenly being replaced by ones relative to the fixed frame.