- #1

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"[tex]\vec{a} = \vec{a'} + 2\vec{\omega} \times \vec{v'} + \vec{\omega} \times (\vec{\omega} \times \vec{r})[/tex]

Multiplying through by mass, m

[tex]m\vec{a} = \vec{F_{ext}} = m\vec{a'} + 2m\vec{\omega} \times \vec{v'} + m\vec{\omega} \times (\vec{\omega} \times \vec{r})[/tex]

We preserve Newton II in rotating frame by writing [tex]\vec{F'_{net}} = m\vec{a'}[/tex] where [tex]\vec{F'_{net}}[/tex] is the net force measured by observer in rotating frame.

ie. [tex]\vec{F'_{net}} = \vec{F_{ext}} - 2m(\vec{\omega} \times \vec{v'}) - m[\vec{\omega} \times (\vec{\omega} \times \vec{r})][/tex]"

It's really the last line that's confusing me. The expressions for the Coriolis and centrifugal forces are

[tex]\vec{F_{Cor}} = -2m(\vec{\omega} \times \vec{v'})[/tex] and [tex]\vec{F_{cent}} = -m\vec{\omega} \times (\vec{\omega} \times \vec{r})[/tex], so why isn't it

[tex]\vec{F'_{net}} - \vec{F_{Cor}} - \vec{F_{cent}} = \vec{F_{ext}}[/tex]?