Particle moving along path, change of angle of inclination

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Homework Help Overview

The discussion revolves around a particle's motion along a path described by the equation y=3x^3. Participants are exploring how to analyze the change of angle of inclination, particularly through the use of polar coordinates and curvature concepts.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the possibility of converting the equation into polar coordinates and express uncertainty about the next steps. There is also mention of using curvature and the relationship between angle and the derivative of the function.

Discussion Status

The conversation is ongoing, with some participants providing hints about curvature and derivatives, while others express confusion about the clarity of the original question. There is an indication of productive direction with suggestions to explore curvature and its relation to the angle of inclination.

Contextual Notes

There are concerns regarding the readability of the original question, which may affect the clarity of the discussion. Participants are encouraged to provide clearer statements to facilitate better assistance.

Unicow
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Homework Statement


upload_2017-7-16_22-57-30.png


Homework Equations


Equation given in question.

The Attempt at a Solution


The only thing I could think of was to try changing the y=3x^3 into polar coordinates but I didn't know where to go from there... Could I get some direction to how I should go about this, I'm sort of stumped as to how I should start this.
 
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Unicow said:

Homework Statement


View attachment 207313

Homework Equations


Equation given in question.

The Attempt at a Solution


The only thing I could think of was to try changing the y=3x^3 into polar coordinates but I didn't know where to go from there... Could I get some direction to how I should go about this, I'm sort of stumped as to how I should start this.

Your "question" is unreadable. You should take the trouble to actually type it out here; many helpers would not look at posted images, even if they were readable.
 
Unicow said:
how I should go about this,
You are given a hint to use curvature. Have you been taught any equations relating to that? See "curvature of a graph" at https://en.m.wikipedia.org/wiki/Curvature.
Or, from first principles, you know ##\theta=\arctan (dy/dx)##. You could find how fast that changes as x changes and divide by how fast distance along the curve changes as x changes.
 
Ray Vickson said:
Your "question" is unreadable.
I agree.
 

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