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Knowledge
The lecture focuses on deriving the Linear Momentum Balance in a cylindrical coordinate system, essential for analyzing deformation in cylindrical bodies. It introduces the concept of basis vectors in cylindrical coordinates, explains the formulation of linear momentum balance, and details the calculation of forces acting on cylindrical elements. Key aspects include using Taylor’s series for stress components and evaluating changes in basis vector orientations, which are crucial for accurate momentum analysis.
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Sections
References
ch17.pdfClass Notes
Memorization
What we have learnt
- The cylindrical coordinate ...
- Basis vectors in cylindrica...
- Using Taylor's series helps...
Final Test
Revision Tests
What we have learnt
- The cylindrical coordinate system is vital for studying deformation in cylindrical shapes.
- Basis vectors in cylindrical coordinates change with the angle θ, affecting the analysis of forces.
- Using Taylor's series helps to approximate varying stress components in the context of cylindrical elements.
Key Concepts
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Term: Cylindrical Coordinate System
Definition: A coordinate system defined by the distance from a reference axis and the angle around that axis, commonly used for cylindrical shapes.
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Term: Basis Vectors
Definition: Vectors that define the coordinate system at a point; in cylindrical coordinates, they vary based on the angle θ.
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Term: Linear Momentum Balance
Definition: A principle stating that the rate of change of momentum of a system equals the sum of the forces acting on it.
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Term: Taylor's Series
Definition: An approximation method used to represent functions as infinite sums of terms calculated from the values of their derivatives at a single point.