A classical mechanics problem involve rotating

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SUMMARY

The discussion focuses on a classical mechanics problem involving rotating systems, specifically analyzing the relationship between radial distance and angular motion. The Coriolis force, defined as F_cor=2mvΩ, and the centrifugal force, F_cf=Ω²mr, are critical in understanding the tangential acceleration and radial distance changes. The participants suggest that the motion may resemble a helix, with x(t) potentially being an exponential function solved by ordinary differential equations (ODEs). The challenge lies in deriving the relationship between y and x from the given equations.

PREREQUISITES
  • Understanding of classical mechanics principles, particularly forces in rotating systems.
  • Familiarity with the Coriolis and centrifugal forces.
  • Knowledge of ordinary differential equations (ODEs) and their applications in motion analysis.
  • Ability to interpret and manipulate polar coordinates (r, φ) in relation to Cartesian coordinates (x, y).
NEXT STEPS
  • Study the application of the Coriolis force in rotating reference frames.
  • Learn how to derive relationships between variables in polar coordinates and Cartesian coordinates.
  • Explore the use of ordinary differential equations (ODEs) in modeling motion in rotating systems.
  • Investigate the characteristics of helical motion and its mathematical representation.
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Students and professionals in physics, particularly those studying mechanics, as well as educators seeking to deepen their understanding of rotating systems and forces involved in motion analysis.

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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