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

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SUMMARY

The discussion clarifies the equation dr/dt = -V in polar coordinates, emphasizing that V represents the velocity of the downward pull on the string, not tangential velocity. The relationship r(t) = V/w(t) is established, indicating that as the vertical string length increases, the radius r decreases. Participants stress the importance of understanding variable definitions in physics equations to avoid misapplication.

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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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