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

In summary, the conversation discusses the calculation of d(r-hat)/d(theta) in cylindrical coordinates, with one person suggesting it is -(theta-hat) and another confirming that it is actually \hat \theta. The conversation ends with gratitude for the clarification.
  • #1
khfrekek1992
30
0

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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  • #2
so theta is moved over by d(theta) shifting over r-hat and theta-hat.. What would d(r-hat)/d(theta) be?
 
  • #3
anyone? :)
 
  • #4
Hi khfrekek1992! :smile:

[tex]{d\hat r \over d\theta} = \hat \theta[/tex]

If you draw [itex]\hat r[/itex] for 2 angles, you'll see that the vector-difference between them points in the direction of [itex]\hat \theta[/itex].
Its (approximate) length is [itex]d\theta[/itex].
 
  • #5
Oh! I see how you get that now.. Thanks so much! That helps a ton :D
 

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

1. What is the formula for finding the change in unit vectors in cylindrical coordinates?

The formula for finding the change in unit vectors in cylindrical coordinates is d(r-hat)/d(theta) = -sin(theta) i-hat + cos(theta) j-hat.

2. Why is there a change in unit vectors in cylindrical coordinates?

There is a change in unit vectors in cylindrical coordinates because the direction of the radius vector changes as the angle increases, causing a change in the direction of the unit vector.

3. How is the change in unit vectors related to the angle in cylindrical coordinates?

The change in unit vectors is directly related to the angle in cylindrical coordinates. As the angle increases, the unit vector changes direction and magnitude, resulting in a change in the unit vector.

4. What is the significance of the negative sign in the formula for the change in unit vectors?

The negative sign in the formula for the change in unit vectors represents the change in direction of the unit vector as the angle increases. This ensures that the unit vector always points in the direction of increasing angle.

5. How can the change in unit vectors be visualized in cylindrical coordinates?

The change in unit vectors can be visualized by imagining a rotating vector at a fixed radius in the cylindrical coordinate system. As the angle increases, the direction of the vector changes, resulting in a change in the unit vector at that point.

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