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PhMichael
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The picture speaks for itself: one man "A" is standing of a rotating disk whose angular velocity is [tex] \omega [/tex] CCW, and another one "B" is standing still on earth. I'm riquired to find the coriolis and centrifugal forces that act on "B" as seen from "A".
Coriolis:
[tex] \vec{F}_{cor} = -2m \vec{\omega} \times \vec{v}_{rel} [/tex]
Centrifugal:
[tex] \vec{F}_{cen} = -m \vec{\omega} \times (\vec{\omega} \times \vec{r}) [/tex]
where,
the angular velocity should be taken in the CW sense, since "A" sees "B" doing circles in that direction, so:
[tex] \vec{\omega}=-\omega \hat{z} [/tex]
about the relative velocity of "B" with respect to "A" I'm not quite sure because the coriolis force appears only when there's movement in a rotating frame, now "A" clearly doesn't move, but the question is: can it see "B" moving in the following velocity:
[tex] \vec{v}_{rel} = \omega r \hat{\theta} [/tex]
??
and the radius vector is:
[tex] \vec{r} = R \hat{r} [/tex]
any clarification would be appreciated =)
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Homework Statement
The picture speaks for itself: one man "A" is standing of a rotating disk whose angular velocity is [tex] \omega [/tex] CCW, and another one "B" is standing still on earth. I'm riquired to find the coriolis and centrifugal forces that act on "B" as seen from "A".
The Attempt at a Solution
Coriolis:
[tex] \vec{F}_{cor} = -2m \vec{\omega} \times \vec{v}_{rel} [/tex]
Centrifugal:
[tex] \vec{F}_{cen} = -m \vec{\omega} \times (\vec{\omega} \times \vec{r}) [/tex]
where,
the angular velocity should be taken in the CW sense, since "A" sees "B" doing circles in that direction, so:
[tex] \vec{\omega}=-\omega \hat{z} [/tex]
about the relative velocity of "B" with respect to "A" I'm not quite sure because the coriolis force appears only when there's movement in a rotating frame, now "A" clearly doesn't move, but the question is: can it see "B" moving in the following velocity:
[tex] \vec{v}_{rel} = \omega r \hat{\theta} [/tex]
??
and the radius vector is:
[tex] \vec{r} = R \hat{r} [/tex]
any clarification would be appreciated =)
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