A classical mechanics problem involve rotating

AI Thread Summary
The discussion revolves around a classical mechanics problem involving rotational dynamics, specifically focusing on the relationship between radial distance and angular motion. The user expresses uncertainty about deriving the relationship y/x and suggests that the motion may resemble a helix, with x(t) potentially being exponential. They mention the influence of Coriolis and centrifugal forces on the radial distance r(t). The conversation emphasizes the importance of using appropriate variables and derivatives to analyze the problem effectively. Overall, the thread highlights the complexities of modeling rotational motion in classical mechanics.
drop_out_kid
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Homework Statement
I intuitively think this is a helix, x(t) probably a exponential solved by ODE, but I cannot come up with it.. I think in this problem. Coriolis force is for tangential acceleration(r(t) increases) and the centrifugal force is making r(t) increases.
Relevant Equations
F_cor=2mv $Omega$
F_cf=$Omega^2$m*r
1650171676464.png


I came up with these: (especially not sure if second is right)
1650171975775.png
 
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From eqs 1 I can get r is exponential, question is to get y/x or other relation from eqs 2
 
drop_out_kid said:
Homework Statement:: I intuitively think this is a helix, x(t) probably a exponential solved by ODE, but I cannot come up with it.. I think in this problem. Coriolis force is for tangential acceleration(r(t) increases) and the centrifugal force is making r(t) increases.
Relevant Equations:: F_cor=2mv $Omega$
F_cf=$Omega^2$m*r

View attachment 300109

I came up with these: (especially not sure if second is right)
View attachment 300110
The instructions are to use x as the radial distance, etc. Turning those into r, phi and using x, y for fixed axes is not going to help.
Start by considering first derivatives, like ##\dot y##.
 
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