- #1
etotheipi
- Homework Statement
- A rotating space station (at ##\omega##) has a radius R. Alice climbs up a tower of height H and drops an object from rest, in the rotating frame. Calculate the velocity and horizontal distance to the tower when it hits the floor. It is given that ##R \gg H##
- Relevant Equations
- N/A
I solved this in an inertial frame, but now I want to do it in the rotating frame. As far as I can tell the equation of motion is $$\vec{F}_{cent} + \vec{F}_{cor} = mr\omega^2 + 2m\vec{v} \times \vec{\omega} = m\frac{d^2\vec{r}}{dt^2}$$The solutions take a different approach. They state that the Coriolis force is $$F_{cor} (t) = 2m \omega^2 R t \omega = 2 m \omega^3 R t$$and they simply integrate this w.r.t. time. There are two things I don't understand. Why have they ignored the centrifugal force (or used it in a weird way, that I can't see), and also where did their expression for the Coriolis force come from? Thanks