22.213 Dynamics

Fall   1999

2000 Catalog: Vector development of kinematics of a particle with respect to rotating and non-rotating frames of reference in one, two, and three dimensions. The dynamics of a particle, system of particles, and rigid bodies. Angular momentum and the inertial properties of rigid bodies. Energy, impulse and momentum. Prerequisites: 22.211.  ( 3 )

Textbook: Riley and Sturges, Engineering Mechanics 2nd. Ed., Dynamics, John Wiley

Coordinator: J. McKelliget, Professor, Mechanical Engineering

 Goals: 

• To develop a firm understanding of the scientific principles of the kinematics of points, systems of particles, and rigid bodies.
• To develop a firm understanding of the scientific principles of the kinetics of particles, systems of particles, and rigid bodies.
• To develop a systematic approach to the solution of engineering problems in the kinematics and kinetics of points, systems of particles, and rigid bodies using a vector formalism.
• To lay the groundwork for subsequent courses in machine dynamics and dynamic systems.
• To teach the student the fundamental concepts involved in the motion of particles, systems of particles, and rigid bodies.
• To teach a consistent methodology that will enable to student to solve a wide range of problems in dynamics. The objective is to stress the similarities between the problems and their solutions, not the differences.

 Objectives:  Upon completion of this course the student will be able to

• Apply the rectilinear motion equations (translational and rotational) to problems in kinematics and kinetics.

• Understand the concepts of normal and tangential acceleration.

• Understand the concepts of relative velocity and acceleration.

• Apply vector principles to analyze the planar kinematics of the slider crank mechanism and the four bar linkage.

• Apply the vector based rotating frames equation to solve kinematic problems involving rotating sliders.

• Set up free body diagrams for rigid bodies.

• State and explain Newton's laws of motion.

• Apply Newton's laws to particles, systems of particles, and rigid bodies in planar motion.

• Apply the moment equation about different points to rigid bodies in planar motion.

• Calculate the moment of inertia of a rigid body and apply the parallel axis theorem.

• Apply the principle of work and energy to planar rigid body problems.

• Apply the principle of conservation of angular momentum to planar rigid body problems.

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Prerequisites by Topic:

•  Solid analytical geometry

•   Basic differentiation and integration

•   Vector notation and algebra

•   Concept of a volume or triple integral

•   Concepts of force and moment of a force

Topics Covered:

•  Kinematics of points (7 classes)

•   Kinematics of rigid bodies in planar motion (11 classes)

•   Kinetics of particles and mass centers (5 classes)

•   Angular Momentum of particles, systems of particles, Euler I (5 classes)

•   Angular Momentum of rigid bodies, Euler II, (6 classes)

•   Work-energy principles, particles, rigid bodies (10 classes)

Evaluation:

Examinations 90%, Homework 10%

Professional Component:

This course forms the foundation for much of the student's knowledge of basic dynamics.  It is key to their successful application of the principals of motion to problems in machine dynamics, vibrations, and fluid motion.  As practicing engineers it is essential that they understand the scientific principles, and the underlying assumptions, that are contained in the equations of mechanics.  The course also gives the student practice in the solution of engineering problems using a well-defined scientific and mathematical methodology.

How course meets Program Objectives (numbers refer to section in SSR): 

• Homework and informational content contribute to fundamental knowledge (2.1-ii)
• Homework and informational content contribute to experience in the integrated application of fundamental principals (2.1-iv)

Specific Objectives:

Prepared by:   John McKelliget                                    Date:  May 2000