A classical mechanics problem involve rotating

In summary, the conversation discusses the problem of finding the relationship between y/x in the context of two equations, where one involves an exponential function and the other involves solving an ODE. The problem also involves the Coriolis and centrifugal forces and their effects on tangential acceleration and radial distance. The use of different variables and axes is also mentioned as a potential challenge. Consideration of first derivatives, specifically ##\dot y##, is suggested as a starting point.
  • #1
drop_out_kid
34
2
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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  • #2
From eqs 1 I can get r is exponential, question is to get y/x or other relation from eqs 2
 
  • #3
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##.
 

FAQ: A classical mechanics problem involve rotating

What is classical mechanics?

Classical mechanics is a branch of physics that studies the motion of objects under the influence of forces. It is based on Newton's laws of motion and is used to describe the behavior of macroscopic objects.

What is rotational motion?

Rotational motion is the movement of an object around an axis or center of rotation. It can be described in terms of angular displacement, velocity, and acceleration.

How is torque related to rotational motion?

Torque is a measure of the force that causes an object to rotate around an axis. It is related to rotational motion through the equation τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration.

What is the difference between angular velocity and linear velocity?

Angular velocity is a measure of how fast an object is rotating around an axis, while linear velocity is a measure of how fast an object is moving in a straight line. Angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

How are rotational and translational motion connected?

Rotational and translational motion are connected through the concept of inertia. An object's moment of inertia determines how it will respond to rotational motion, while its mass determines how it will respond to translational motion. In a rigid body, rotational and translational motion are always coupled.

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