Solid Mechanics | 6. Angular Momentum Balance by Abraham | Learn Smarter
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge
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.

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

  • 1

    Angular Momentum Balance

    This section discusses the balance of angular momentum in a cuboidal mass, detailing contributions from traction and body forces, dynamics terms, and simplifying assumptions in derivation.

    Learning Practice

  • 1.1

    Traction Contribution

    The section discusses the derivation of angular momentum balance, emphasizing the role of traction forces and their contributions to torque.

    Learning Practice

  • 1.2

    Body Force Contribution

    This section discusses the contribution of body forces to angular momentum balance in the context of solid mechanics.

    Learning Practice

  • 1.3

    Dynamics Term

    This section addresses the derivation of the dynamics term in the balance of angular momentum, focusing on the integration of mass particles' contributions to angular momentum in a cuboidal volume.

    Learning Practice

  • 1.4

    Final Balance

    The section discusses the derivation of the Angular Momentum Balance (AMB) equation and its significance in analyzing the effects of external forces on a cuboid.

    Learning Practice

  • 1.5

    Representation In A Coordinate System

    This section discusses how to represent the angular momentum balance equation in component form within a specified coordinate system.

    Learning Practice

  • 1.6

    An Alternate Method To Derive Amb

    This section provides an alternative approach to derive the Angular Momentum Balance (AMB) using approximate methods applicable to a cuboidal element.

    Learning Practice

  • 2

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

    This section discusses how externally applied distributed loads on a body relate to the stress tensor, with focus on deriving the relationships for stress equilibrium.

    Learning Practice

  • 2.1

    Relating Stress Matrix At Surface Point With Externally Applied Load

    This section discusses the relationship between the stress matrix at a surface point of a body and the externally applied load, highlighting how traction influences stress distribution.

    Learning Practice

  • 3

    Traction And Stress Inside A Fluid Body At Rest

    This section explains the concepts of traction and stress in a static fluid, emphasizing how pressure relates to these forces.

    Learning Practice

  • 3.1

    Traction

    This section discusses the role of traction in the balance of angular momentum within solid mechanics, highlighting how traction contributions affect torque and stress in rigid bodies.

    Learning Practice

  • 3.2

    Stress

    This section delves into the concept of stress, its derivation, and its applications in relation to angular momentum and body forces.

    Learning Practice

References

ch6.pdf

Class Notes

Memorization

What we have learnt

  • Angular momentum balance ca...
  • The stress matrix must rema...
  • The pressure within a fluid...

Final Test

Revision Tests