Unit vector in polar coorindate

Click For Summary

Discussion Overview

The discussion revolves around the representation of vectors in polar coordinates, particularly how to interpret and convert vectors from rectangular coordinates to polar coordinates. Participants explore the meanings of components in both coordinate systems and seek clarification on the conversion process.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant questions whether the expression 3r + 1θ in polar coordinates represents a line with length 3 from the origin and an angle of 1 radian from the x-axis.
  • Another participant agrees with the interpretation of 3r + 1θ as indicating three "steps" away from the origin and one "step" counter-clockwise from the x-axis.
  • A participant asks how to convert the vector 3i + j from rectangular coordinates to polar coordinates.
  • One response explains that the radius in polar coordinates is the magnitude of the position vector, calculated as r = |3i + j| = √10, and that the angle θ can be found using θ = arctan(y/x) = arctan(1/3).
  • Another participant expresses uncertainty about the topic and indicates they have further questions.
  • A later reply mentions the unit vector eθ as representing an "additional" rotation from the vector er, linking to a visual reference for clarification.

Areas of Agreement / Disagreement

Participants generally agree on the basic interpretation of polar coordinates but express varying levels of understanding and familiarity with the topic. Some questions remain unresolved, particularly regarding the conversion process and the implications of the unit vectors.

Contextual Notes

Participants note the importance of understanding the relationship between rectangular and polar coordinates, including the need to adjust angles based on the quadrant in which the point lies. There are references to external resources for further clarification.

Who May Find This Useful

This discussion may be useful for students or individuals seeking to understand the conversion between rectangular and polar coordinates, as well as those interested in the geometric interpretation of vectors in different coordinate systems.

athrun200
Messages
275
Reaction score
0
In rectangular corr. 3i+j mean leght in x-direction =3 in y-3direction =1

However, how about in polar coorindate?
3r+1[itex]\theta[/itex] (r and [itex]\theta[/itex] are the unit verctor in polar coor., I don't know how to type it out, I hope you understand.)

Dose it mean a line with length 3 from origin and angle 1 radian from x-axis?
 
Mathematics news on Phys.org
athrun200 said:
In rectangular corr. 3i+j mean leght in x-direction =3 in y-3direction =1

However, how about in polar coorindate?
3r+1[itex]\theta[/itex] (r and [itex]\theta[/itex] are the unit verctor in polar coor., I don't know how to type it out, I hope you understand.)

Dose it mean a line with length 3 from origin and angle 1 radian from x-axis?
Yes, just as 3i+j means three "steps" in the x-direction and 1 "step" in the y-direction, 3r + 1[itex]\theta[/itex] means three "steps" away from the origin and 1 "step" counter-clockwise from the x-axis.
 
Hootenanny said:
Yes, just as 3i+j means three "steps" in the x-direction and 1 "step" in the y-direction, 3r + 1[itex]\theta[/itex] means three "steps" away from the origin and 1 "step" counter-clockwise from the x-axis.

How to convert the vector in retangular corrdinate to polar coordinate?
For example, 3i+j, how to write in polar corrdinate unit vector?
 
For a detailed explanation see here: http://en.wikipedia.org/wiki/Polar_coordinate_system

In polar coordinates, the radius is simply the distance from the origin (i.e. the magnitude of your position vector). So in your example, [itex]r = |3\hat{i} + \hat{j}| = \sqrt{10}[/itex]. The angular component is simply the angle between your vector and the positive x-direction. Since your point is in the first quadrant, this is simply [itex]\theta=\arctan(y/x) = \arctan(1/3)[/itex]. If your point were to be in a different quadrant, you would have to adjust accordingly.
 
I am still very unfamiliar with this new topic, and I still have a lot of question marks in my head.

The details of my reply please refer to my attachment
 

Attachments

  • 1.jpg
    1.jpg
    31.1 KB · Views: 453
athrun200 said:
I am still very unfamiliar with this new topic, and I still have a lot of question marks in my head.

The details of my reply please refer to my attachment
The unit vector [itex]\vex{e}_\theta[/itex] represents an "additional" rotation from the vector [itex]\vec{e}_r[/itex]. Notice that the unit vector [itex]\vec{e}_r[/itex] is the direction from the origin to the point in space [itex]\vec{r}[/itex]: http://en.wikipedia.org/wiki/File:Polar_unit_vectors.PNG.
 

Similar threads

High School To calculate the polar unit vectors using rotated coordinates
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Converting this vector into polar form
  • · Replies 4 ·
Replies
4
Views
2K
High School Why Do We Draw Dimensionless Unit Vectors in Diagrams?
  • · Replies 16 ·
Replies
16
Views
4K
Units for a vector magnitude in the s-plane
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Units of a vector in a velocity vs time graph?
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Transforming coordinates between Cartesian and spherical
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Polar coordinates and unit vectors
  • · Replies 10 ·
Replies
10
Views
4K
Help about the unit vectors for polar coordinates in terms of i and j
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Advantages of Polar Coordinate System & Rotating Unit Vectors
  • · Replies 7 ·
Replies
7
Views
3K
Writing a vector parallel and normal to a unit vector ##\hat n##
  • · Replies 26 ·
Replies
26
Views
3K