Another change in unit vectors (d(r-hat)/d(theta)) in Cylindrical

AI Thread Summary
In cylindrical coordinates, the derivative of the unit vector r-hat with respect to theta, d(r-hat)/d(theta), is equal to the unit vector theta-hat. This relationship arises because as theta changes, the r-hat vector shifts, and the vector difference between two r-hat vectors at different angles points in the direction of theta-hat. The length of this vector difference is approximately d(theta). This understanding clarifies the relationship between the unit vectors in cylindrical coordinates. The discussion effectively resolves the initial query about the derivative of r-hat.
khfrekek1992
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Homework Statement



Does anyone know what d(r-hat)/d(theta) in Cylindrical coordinates is?


Homework Equations





The Attempt at a Solution



I'm pretty sure its -(theta-hat) but I'm not sure, any help?

Thanks so much
 
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so theta is moved over by d(theta) shifting over r-hat and theta-hat.. What would d(r-hat)/d(theta) be?
 
anyone? :)
 
Hi khfrekek1992! :smile:

{d\hat r \over d\theta} = \hat \theta

If you draw \hat r for 2 angles, you'll see that the vector-difference between them points in the direction of \hat \theta.
Its (approximate) length is d\theta.
 
Oh! I see how you get that now.. Thanks so much! That helps a ton :D
 

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