- #31
IPTV013
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The title of the book is : Classical Mechanics by John R. Taylor.
Radius vector in cylindrical coordinates
- Context: Undergrad
- Thread starter Oliver321
- Start date
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Discussion Overview
The discussion revolves around the representation of the radius vector in cylindrical coordinates, specifically addressing the components of the vector and the necessity of basis vectors in this coordinate system. Participants explore the mathematical and conceptual implications of using cylindrical coordinates in physics, particularly in the context of symmetry and dimensionality.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- Some participants express confusion about the representation of the radius vector ##\vec r = z \hat{z} + \rho \hat{\rho}##, questioning why the angle ##\phi## is not included in the equation.
- Others clarify that while ##\hat{z}## is a constant unit vector, ##\hat{\rho}## is not, as its direction depends on ##\phi##.
- Some participants argue that in cases of cylindrical symmetry, it is common for quantities to not depend on ##\phi##, allowing for a two-dimensional description using only ##\hat{\rho}## and ##\hat{z}##.
- A later reply suggests that the choice of coordinate system should reflect the symmetry of the problem, which may lead to reducing the number of coordinates needed.
- Participants discuss the implications of including the term with ##\phi## and whether it would affect the solution to the exercise presented.
Areas of Agreement / Disagreement
Participants generally agree that the radius vector can be expressed in terms of two basis vectors under certain conditions, particularly in cylindrical symmetry. However, there is no consensus on the necessity of including the ##\phi## component in all cases, and some participants remain uncertain about the implications of omitting it.
Contextual Notes
Some participants note that the mathematical concept of basis vectors may not align with the physical representation in cylindrical coordinates, leading to confusion about the completeness of the vector representation.
Who May Find This Useful
This discussion may be useful for students and individuals learning about cylindrical coordinates in physics, particularly those grappling with the concepts of vector representation and dimensionality in different coordinate systems.
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