Solid Mechanics | 6. Angular Momentum Balance by Abraham | Learn Smarter
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6. Angular Momentum Balance

6. Angular Momentum Balance

The chapter delves into the balance of angular momentum, detailing the contributions of traction and body forces. It explores the dynamics of deriving the angular momentum balance equation and its representation in a coordinate system, culminating in a symmetric stress tensor outcome. Furthermore, it discusses the relationship between externally applied loads and the stress matrix within a fluid body at rest, integrating fundamental principles of mechanics and fluid dynamics.

12 sections

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Sections

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  1. 1
    Angular Momentum Balance

    This section discusses the balance of angular momentum in a cuboidal mass,...

  2. 1.1
    Traction Contribution

    The section discusses the derivation of angular momentum balance,...

  3. 1.2
    Body Force Contribution

    This section discusses the contribution of body forces to angular momentum...

  4. 1.3
    Dynamics Term

    This section addresses the derivation of the dynamics term in the balance of...

  5. 1.4
    Final Balance

    The section discusses the derivation of the Angular Momentum Balance (AMB)...

  6. 1.5
    Representation In A Coordinate System

    This section discusses how to represent the angular momentum balance...

  7. 1.6
    An Alternate Method To Derive Amb

    This section provides an alternative approach to derive the Angular Momentum...

  8. 2
    Relating Externally Applied Distributed Load On Body's Surface To Stress Tensor

    This section discusses how externally applied distributed loads on a body...

  9. 2.1
    Relating Stress Matrix At Surface Point With Externally Applied Load

    This section discusses the relationship between the stress matrix at a...

  10. 3
    Traction And Stress Inside A Fluid Body At Rest

    This section explains the concepts of traction and stress in a static fluid,...

  11. 3.1

    This section discusses the role of traction in the balance of angular...

  12. 3.2

    This section delves into the concept of stress, its derivation, and its...

What we have learnt

  • Angular momentum balance can be derived considering both traction and body force contributions.
  • The stress matrix must remain symmetric, even under the influence of external forces or acceleration.
  • The pressure within a fluid body at rest generates traction that aligns with the normal to the surfaces of the fluid.

Key Concepts

-- Angular Momentum Balance
A principle in mechanics that equates the sum of angular momentum contributions from various forces, including traction forces and body forces.
-- Stress Matrix
A mathematical representation of stress states within a material, capturing internal forces acting on a differential volume element.
-- Traction
Force per unit area acting on a material surface, essential for understanding how external loads affect internal stress states.
-- Fluid Statics
The study of fluids at rest, emphasizing the role of pressure and its effects on forces within fluids.

Additional Learning Materials

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