Engineering Mechanics | Rigid Body Motion in the Plane by Pavan | Learn Smarter
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Rigid Body Motion in the Plane

Rigid body motion encompasses several forms of movement, including translation and rotation in a plane. Angular kinematics describes the relationship between angular displacement, velocity, and acceleration. The chapter also delves into angular momentum and Euler’s laws of motion, providing a foundation for understanding the dynamics of rigid bodies.

Sections

  • 1

    Definition: Rigid Body Motion

    Learning

  • 1.1

    Translation

    This section introduces rigid body motion, focusing on translation, rotation, and general motion in the plane.

    Learning Practice

  • 1.2

    Rotation

    This section focuses on the concept of rotation in rigid bodies, including key kinematic equations and the fundamentals of angular momentum.

    Learning Practice

  • 1.3

    General Motion

    This section discusses general motion of rigid bodies, including translation, rotation, and their combination.

    Learning Practice

  • 2

    Rotation In The Plane

    This section elaborates on the kinematics of rotation in a plane, detailing angular displacement, velocity, acceleration, and the relation to linear motion.

    Learning Practice

  • 2.1

    Kinematics

    This section covers the fundamentals of kinematics in rigid body motion, including concepts of angular displacement, velocity, and acceleration.

    Learning Practice

  • 3

    Kinematics In A Rotating And Translating Frame (Planar Motion)

    This section explores the kinematics of rigid body motion in two dimensions, focusing on the analysis of translation and rotation.

    Learning Practice

  • 4

    Angular Momentum Of A Rigid Body (Planar Motion)

    This section explores the concept of angular momentum in rigid body planar motion, focusing on its calculation and significance.

    Learning Practice

  • 4.1

    Translational Part

    This section covers the fundamental concepts of rigid body motion in a plane, focusing on translational and rotational motion, angular momentum, and Euler's laws.

    Learning Practice

  • 4.2

    Rotational Part

    This section explores the dynamics of rigid body motion, focusing on rotation, angular momentum, and Euler's laws.

    Learning Practice

  • 5

    Euler’s Laws Of Motion

    Euler’s Laws of Motion describe the relationship between forces and the motion of rigid bodies, focusing on linear momentum and angular momentum.

    Learning Practice

  • 5.1

    First Law

    Euler's First Law describes how the linear momentum of a rigid body's center of mass changes in response to external forces.

    Learning Practice

  • 5.2

    Second Law

    Euler's Second Law describes the relationship between the rate of change of angular momentum and external torque acting on a rigid body.

    Learning Practice

  • 5.3

    Third Law (Torque Form Of Newton’s 3rd Law)

    The third law of motion focuses on internal forces in a rigid body, emphasizing that they do not contribute to the net torque about the center of mass.

    Learning Practice

  • 6

    Independence From Newton’s Laws

    Euler's laws provide a framework for analyzing rigid body motion, particularly with angular momentum, independent of Newton's laws.

    Learning Practice

  • 7

    Examples And Applications

    This section discusses the various examples and applications of rigid body motion, highlighting key principles of translation and rotation.

    Learning Practice

  • 7.1

    Rolling Without Slipping

    This section explores the concept of rigid body motion, focusing on the relationship between translation and rotation of bodies rolling without slipping.

    Learning Practice

  • 7.2

    Disk Rotating And Translating

    This section covers the motion of a rigid body, specifically focusing on the principles of rotation and translation in the context of a disk.

    Learning Practice

  • 7.3

    Pendulum-Like Motion Of A Rod

    This section discusses the pendulum-like motion of a rod pivoted at one end as it rotates in a vertical plane.

    Learning Practice

  • 7.4

    Spinning Gears

    This section introduces spinning gears as an example of rigid body motion, highlighting their role in transmitting torque and angular momentum.

    Learning Practice

  • 8

    Summary Table

    This section provides a concise summary of the key equations and principles related to the motion of rigid bodies in a plane.

    Learning Practice

References

Module V_ Rigid Body Motion in the Plane.pdf

Class Notes

Memorization

What we have learnt

  • A rigid body maintains cons...
  • Angular kinematics defines ...
  • Euler’s laws extend Newtoni...

Final Test

Revision Tests