Generalized coordinates- scalar product

Click For Summary
SUMMARY

The discussion focuses on calculating the scalar product of the vector (0,1) in plane polar coordinates, which is determined to be r² using the equation AαgαβBβ. Additionally, the unit vector in the θ direction is queried, emphasizing the need to understand the properties of unit vectors in polar coordinates. The solution for part a is confirmed, while part b remains unresolved, highlighting a gap in understanding unit vector components.

PREREQUISITES
  • Understanding of plane polar coordinates
  • Familiarity with scalar product calculations
  • Knowledge of unit vectors and their properties
  • Basic grasp of tensor notation in physics
NEXT STEPS
  • Study the derivation of scalar products in polar coordinates
  • Learn about unit vectors in different coordinate systems
  • Explore the concept of metric tensors and their applications
  • Review vector calculus, focusing on polar coordinates
USEFUL FOR

Students in physics or engineering, particularly those studying mechanics or vector calculus, will benefit from this discussion as it addresses fundamental concepts in vector analysis and coordinate transformations.

JimKC
Messages
1
Reaction score
0

Homework Statement


a: In plane polar coordinates, find the scalar product of the vector (0,1) with itself.
b: What would be the r, θ components of the unit vector in the θ direction?

Homework Equations


Scalar product of 2 vectors = AαgαβBβ

The Attempt at a Solution


For part a, I used the equation above to determine the scalar product of (0,1) with itself is r2.
Assuming that's correct, I'm really stuck on part b and not sure what to do.
 
Physics news on Phys.org
It's pretty much the same as the question "what is the length of a unit vector?". You should know an answer to that.
 
  • Like
Likes   Reactions: Orodruin and berkeman

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
Replies
13
Views
2K
  • · Replies 1 ·
Replies
1
Views
8K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 36 ·
2
Replies
36
Views
6K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
26
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K