Why Is the Polar Form of the Position Vector Defined as r = r\vec{r}?

  • Thread starter Thread starter sherlockjones
  • Start date Start date
  • Tags Tags
    Kinematics Polar
Click For Summary
SUMMARY

The polar form of the position vector is defined as r = r\vec{r} to express the position in terms of its magnitude (r) and direction (θ). The position vector \vec{r} can be represented in Cartesian coordinates as \vec{r} = x\vec{i} + y\vec{j}, where r is the magnitude calculated as r = √(x² + y²). In polar coordinates, the two parameters required to define a position are indeed r and θ, which correspond to the radial distance and the angle from the positive x-axis, respectively.

PREREQUISITES
  • Understanding of Cartesian coordinates and vectors
  • Familiarity with polar coordinates and their conversion
  • Knowledge of trigonometric functions
  • Basic vector operations in physics or mathematics
NEXT STEPS
  • Study the conversion formulas between Cartesian and polar coordinates
  • Learn about vector magnitude and direction in physics
  • Explore the applications of polar coordinates in complex numbers
  • Investigate the use of polar coordinates in calculus, particularly in integration
USEFUL FOR

Students of mathematics and physics, educators teaching coordinate systems, and anyone interested in vector analysis and its applications in various fields.

sherlockjones
Messages
31
Reaction score
0
If we have a position vector [tex]\vec{r} = x\vec{i} + y\vec{j}[/tex] why is the polar form of the equation [tex]r = r\vec{r}[/tex]? Don't we need two parameters to define a postition? And [tex]r[/tex] is the magnitude of [tex]\vec{r}[/tex]?

Thanks
 
Physics news on Phys.org
sherlockjones said:
If we have a position vector [tex]\vec{r} = x\vec{i} + y\vec{j}[/tex] why is the polar form of the equation [tex]r = r\vec{r}[/tex]? Don't we need two parameters to define a postition? And [tex]r[/tex] is the magnitude of [tex]\vec{r}[/tex]?

Thanks
The two parameters are [itex]r[/itex] and [itex]\theta[/itex].

http://mathworld.wolfram.com/PolarCoordinates.html
 

Similar threads

Replies
1
Views
3K
Replies
3
Views
1K
Replies
2
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
2
Views
2K
  • · Replies 16 ·
Replies
16
Views
2K
  • · Replies 12 ·
Replies
12
Views
2K
Replies
1
Views
1K
Replies
12
Views
2K