Why Is dr/dt=-V in Polar Coordinates?

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around the equation dr/dt = -V in the context of polar coordinates, particularly focusing on the interpretation of variables involved in a physics problem related to motion and string dynamics. Participants explore the implications of this equation and the definitions of the variables used.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants express confusion regarding the equation dr/dt = -V, questioning how this relationship can be valid given their understanding of r(t) = V/w(t).
  • Others note that as the vertical string gets longer, the radius r decreases, which adds to the confusion about the relationship between r and V.
  • One participant emphasizes the importance of understanding the definitions of variables in physics, clarifying that V in this context is not the tangential velocity but rather the velocity of the downward pull on the string.
  • Another participant acknowledges that their assumption of V being equal to rw, as commonly seen in circular motion problems, led to incorrect conclusions in their calculations.

Areas of Agreement / Disagreement

Participants generally do not reach a consensus on the interpretation of the equation dr/dt = -V, with multiple competing views regarding the definitions and implications of the variables involved.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the variables, particularly the interpretation of V and its relationship to r and w. The discussion does not resolve these ambiguities.

Andrax
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wPdNsUI.png

In the solution , it says we have dr/dt= -V (polar coordinates)
How? i can't see how this can be possible , we know that r(t)=V/w(t), and that's it .
 
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Andrax said:
wPdNsUI.png

In the solution , it says we have dr/dt= -V (polar coordinates) How? i can't see how this can be possible ,
r gets smaller as the vertical string gets longer.

Andrax said:
we know that r(t)=V/w(t), and that's it .
Why?
 
You have to be careful when using equations in physics. You cannot just blindly plug in variables, you need to know what each variable means.

In this problem V is NOT the tangential velocity so V is not equal to rw as it is in many circular motion problems. Here V is the velocity of the downward pull on the string.
 
DaleSpam said:
You have to be careful when using equations in physics. You cannot just blindly plug in variables, you need to know what each variable means.

In this problem V is NOT the tangential velocity so V is not equal to rw as it is in many circular motion problems. Here V is the velocity of the downward pull on the string.

thank you , the differential equations gives me w(t)=2 if i use V=rw , i just presumed that since it's alays used in these kind of problems
 

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