Newton's Laws, Vectors, and Reference Frames · Lecture Videos
MIT OpenCourseWare
Engineering Dynamics
- Instructors
- Prof. J. Kim Vandiver, Prof. David Gossard
- Term
- Fall 2011
- Level
- Undergraduate
- What's inside
- 223 videos · 11 problem sets · 6 exams · 25 solutions · 2 handouts · 234 other files · 15 web pages
- Materials open
- Videos here · files on MIT OCW
About this course
Source: MIT OpenCourseWare 2.003SC Engineering Dynamics, Fall 2011, Prof. J. Kim Vandiver, Prof. David Gossard — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Learn one topic
12 concept pages, one per MIT session: the clips, notes and practice for that topic. MIT solutions for 10 of 12 topics.
All 12 topics
- Newton's Laws, Vectors, and Reference Frames MIT solutions
- Velocity, Acceleration, and Rotational Motion MIT solutions
- Angular Momentum and Torque MIT solutions
- Free Body Diagrams and Fictitious Forces MIT solutions
- Angular Momentum and Rotating Masses
- Angular Momentum and Motion of Rotating Rigid Bodies MIT solutions
- Finding Equations of Motion for Rigid Body Rotation MIT solutions
- Lagrange Equations MIT solutions
- Mechanical Vibration MIT solutions
- Reducing Problem Vibration and Intro to Multi-DOF Vibration
- Vibration of Multi-Degree-of-Freedom Systems MIT solutions
- Vibration Analysis by Mode Superposition MIT solutions
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- This course has 157 videos, each embedded on its own MIT page, across 14 sections. They're shown in MIT's listing order within each section. A verified course-wide order is not claimed for this course.
Not included here
16 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (12 items)
- Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (4 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Newton's Laws, Vectors, and Reference Frames
- Kinematics Handout Download
- Problem Set 1 Download
- Problem Set 1 Concept Question Solutions Download
- Problem Set 1 Solutions Download
- Modeling in dynamics Open ↗
- Purpose of concept questions Open ↗
Velocity, Acceleration, and Rotational Motion
- Problem Set 2 Download
- Problem Set 2 Concept Question Answer Key Download
- Problem Set 2 Solutions Download
- Recitation 2 Notes: Planar Motion Download
- Problem solving with an example of a block on a slope Open ↗
- Vector form of velocity and acceleration in a translating and rotating coordinate system and the expression of them in polar and cylindrical coordinates Open ↗
- Notation Systems Open ↗
Angular Momentum and Torque
- Lecture outline and Use of tangential and normal coordinates with an example Open ↗
- Intro to the time rate of change of linear and angular momentum for a particlecoordinates Open ↗
Free Body Diagrams and Fictitious Forces
Angular Momentum and Rotating Masses
Angular Momentum and Motion of Rotating Rigid Bodies
Finding Equations of Motion for Rigid Body Rotation
Lagrange Equations
Lagrange Equations Continued
Quiz Review Lecture & Quiz 2
Mechanical Vibration
- Concept question discussion of Problem set 9-keep Open ↗
- Introduction to the single degree of freedom (SDOF) system Open ↗
Reducing Problem Vibration and Intro to Multi-DOF Vibration
Vibration of Multi-Degree-of-Freedom Systems
- Problem Set 10 Download
- Problem Set 10 Concept Question Answer Key Download
- Problem Set 10 Solutions Download
- Recitation 11 Notes: Double Pendulum System Download
- Review of the concept questions with Homework 10 Open ↗
- The modal expansion theorem Open ↗
Vibration Analysis by Mode Superposition
- Problem Set 11 Download
- Problem Set 11 Concept Question Answer Key Download
- Problem Set 11 Solutions Download
- Recitation 12 Notes: Modal Analysis Download
- Outline of the final three lectures Open ↗
- Discussion of problem set concept questions Open ↗
- Demonstration of wave propagation on a long string Open ↗
Resource Index
34 files
- Final exam solutions Download
- Problem Set 3 Download
- Problem Set 3 Concept Question Answer Key Download
- Problem Set 3 Solutions Download
- Problem Set 4 Download
- Problem Set 4 Concept Question Answer Key Download
- Problem Set 4 Solutions Download
- Problem Set 5 Download
- Problem Set 5 Concept Question Answer Key Download
- Problem Set 5 Solutions Download
- Problem Set 6 Download
- Problem Set 6 Concept Question Answer Key Download
- Problem Set 6 Solutions Download
- Problem Set 7 Download
- Problem Set 7 Concept Question Answer Key Download
- Problem Set 7 Solutions Download
- Problem Set 8 Download
- Problem Set 8 Solutions Download
- Problem Set 9 Download
- Problem Set 9 Concept Question Answer Key Download
- Problem Set 9 Solutions Download
- Quiz 1 Download
- Quiz 1 Solutions Download
- Quiz 2 Download
- Quiz 2 Solutions Download
- Quiz 3 Download
- Recitation 3 Notes: V and A of a Point in a Moving Frame Download
- Recitation 4 Notes: Torque and Angular Momentum, Pendulum with Torsional Spring, Rolling Pipe on Moving Truck Download
- Recitation 5 Notes: Torque and Angular Momentum, Equations of Motion for Multiple Degree-of-Freedom Systems Download
- Recitation 6 Notes: Moment of Inertia and Imbalance, Rotating Slender Rod Download
- Recitation 7 Notes: Equations of Motion for Cart & Pendulum (Lagrange) Download
- Recitation 8 Notes: Cart and Pendulum (Lagrange) Download
- Recitation 9 Notes: Generalized Forces with Double Pendulum Example Download
- Recitation 10 Notes: Natural Frequency From Deflection & Frequency Response Download
39 videos
- Lecture 1: History of Dynamics; Motion in Moving Reference Frames Open ↗
- Lecture 2: Newton's Laws and Describing the Kinematics of Particles Open ↗
- Lecture 3: Motion of Center of Mass; Acceleration in Rotating Ref. Frames Open ↗
- Lecture 4: Movement of a Particle in Circular Motion w/ Polar Coordinates Open ↗
- Lecture 5: Impulse, Torque, and Angular Momentum for a System of Particles Open ↗
- Lecture 6: Torque and the Time Rate of Change of Angular Momentum Open ↗
- Lecture 7: Degrees of Freedom, Free Body Diagrams, and Fictitious Forces Open ↗
- Lecture 8: Fictitious Forces and Rotating Mass Open ↗
- Lecture 9: Rotating Imbalance Open ↗
- Lecture 10: Equations of Motion, Torque, Angular Momentum of Rigid Bodies Open ↗
- Lecture 11: Mass Moment of Inertia of Rigid Bodies Open ↗
- Lecture 12: Problem Solving Methods for Rotating Rigid Bodies Open ↗
- Lecture 13: Four Classes of Problems With Rotational Motion Open ↗
- Lecture 14: More Complex Rotational Problems and Their Equations of Motion Open ↗
- Lecture 15: Introduction to Lagrange With Examples Open ↗
- Lecture 16: Kinematic Approach to Finding Generalized Forces Open ↗
- Lecture 17: Practice Finding EOM Using Lagrange Equations Open ↗
- Lecture 18: Quiz Review From Optional Problem Set 8 Open ↗
- Lecture 19: Introduction to Mechanical Vibration Open ↗
- Lecture 20: Linear System Modeling a Single Degree of Freedom Oscillator Open ↗
- Lecture 21: Vibration Isolation Open ↗
- Lecture 22: Finding Natural Frequencies and Mode Shapes of a 2 DOF System Open ↗
- Lecture 23: Vibration by Mode Superposition Open ↗
- Lecture 24: Modal Analysis: Orthogonality, Mass Stiffness, Damping Matrix Open ↗
- Lecture 25: Modal Analysis: Response to IC's and to Harmonic Forces Open ↗
- Lecture 26: Response of 2-DOF Systems by the Use of Transfer Functions Open ↗
- Lecture 27: Vibration of Continuous Structures: Strings, Beams, Rods, etc. Open ↗
- Recitation 2: Velocity and Acceleration in Translating and Rotating Frames Open ↗
- Recitation 3: Motion in Moving Reference Frames Open ↗
- Recitation 4: Free Body Diagrams Open ↗
- Recitation 5: Equations of Motion Open ↗
- Recitation 6: Angular Momentum and Torque Open ↗
- Recitation 7: Cart and Pendulum, Direct Method Open ↗
- Recitation 8: Cart and Pendulum, Lagrange Method Open ↗
- Recitation 9: Generalized Forces Open ↗
- Recitation 10: Steady State Dynamics Open ↗
- Recitation 11: Double Pendulum System Open ↗
- Recitation 12: Modal Analysis of a Double Pendulum System Open ↗
- Notation Systems Open ↗
Other materials from this course
223 video transcripts
- Transcript for Candy shooter example of coriolis force done in polar coordinates, full lecture Download
- Transcript for Hockey puck by Lagrange, full lecture Download
- Transcript for Lecture 2: Newton's Laws and Describing the Kinematics of Particles Download
- Transcript for Lecture 2: Newton's Laws and Describing the Kinematics of Particles Download
- Transcript for Problem 1-Sticking sliding in circular track, full lecture Download
- Transcript for Kinematics: derivative of a rotating vector in cylindrical coordinates, full lecture Download
- Transcript for Orthogonality and the computation of the mass and stiffness matrices, full lecture Download
- Transcript for Lecture 3: Motion of Center of Mass; Acceleration in Rotating Ref. Frames Download
- Transcript for Lecture 22: Finding Natural Frequencies and Mode Shapes of a 2 DOF System Download
- Transcript for Damped response of spring-mass-dashpot system to initial conditions, full lecture Download
- Transcript for Dealing with damping in modal analysis, full lecture Download
- Transcript for Recitation 2: Velocity and Acceleration in Translating and Rotating Frames Download
- Transcript for Example 3b: Computing external and internal structural torques using dh / dt; angular momentum vector not aligned with the axis of rotation, full lecture Download
- Transcript for Example computation of Izz for a disk, full lecture Download
- Transcript for Recitation 10: Steady State Dynamics Download
- Transcript for An example deriving equations of motion using Newton's laws, full lecture Download
- Transcript for Response of the SDOF system to initial conditions, full lecture Download
- Transcript for Static and dynamic imbalance definitions, full lecture Download
- Transcript for Lecture 8: Fictitious Forces and Rotating Mass Download
- Transcript for Lecture 19: Introduction to Mechanical Vibration Download
- Transcript for Example 3: Rod leaning on a wall, full lecture Download
- Transcript for Center of percussion problem, full lecture Download
- Transcript for Recitation 9: Generalized Forces Download
- Transcript for Demonstration of a dynamic absorber using a strobe and a vibrating beam, full lecture Download
- Transcript for Vector form of velocity and acceleration in a translating and rotating coordinate system and the expression of them in polar and cylindrical coordinates, full lecture Download
- Transcript for Demo of cart on incline with water in container, full lecture Download
- Transcript for Complete fictitious force discussion, full lecture Download
- Transcript for Finding the response of a pendulum to initial conditions, full lecture Download
- Transcript for Demonstration of wave propagation on a long string, full lecture Download
- Transcript for Definition of moment of inertia matrix, full lecture Download
- Transcript for Intro to the time rate of change of linear and angular momentum for a particlecoordinates, full lecture Download
- Transcript for Base motion Hx/y transfer function-vibration isolation system design, full lecture Download
- Transcript for Recitation 12: Modal Analysis of a Double Pendulum System Download
- Transcript for The definition of center of mass, full lecture Download
- Transcript for New formula for computing torque about moving points, full lecture Download
- Transcript for Generalized coordinate definitions, full lecture Download
- Transcript for Obtain the equations of motion of a 2 DOF system, full lecture Download
- Transcript for Lecture 9: Rotating Imbalance Download
- Transcript for Experimental determination of damping ratio, full lecture Download
- Transcript for Example 2: EOM for Atwoods machine, full lecture Download
- Transcript for Euler's formula for complex numbers, full lecture Download
- Transcript for Free body diagrams with two bodies, full lecture Download
- Transcript for Lecture 4: Movement of a Particle in Circular Motion w/ Polar Coordinates Download
- Transcript for Analysis of the response of a 2-DOF system to harmonic excitation by means of transfer functions and the introduction of the application of the dynamic absorber to mitigate problem vibration, full lecture Download
- Transcript for Example 2a-Pulling the string from a rotating mass through a hole at the axis of rotation. Conservation of angular momentum, h, full lecture Download
- Transcript for Recitation 5: Equations of Motion Download
- Transcript for The modal expansion theorem, full lecture Download
- Transcript for The definition of the angular momentum of a particle with respect to a moving reference point, full lecture Download
- Transcript for Lecture 27: Vibration of Continuous Structures: Strings, Beams, Rods, etc. Download
- Transcript for Rotating mass demo related to homework 1, full lecture Download
- Transcript for Lecture 20: Linear System Modeling a Single Degree of Freedom Oscillator Download
- Transcript for Lecture 20: Linear System Modeling a Single Degree of Freedom Oscillator Download
- Transcript for Lecture 23: Vibration by Mode Superposition Download
- Transcript for Modeling in dynamics, full lecture Download
- Transcript for Examples: Atwood's machine and falling stick, full lecture Download
- Transcript for Lecture 26: Response of 2-DOF Systems by the Use of Transfer Functions Download
- Transcript for Equations of motion (EOM) and degrees of freedom (DOF), full lecture Download
- Transcript for Engineers approach to the solution of the 2nd order differential equation with initial conditions, full lecture Download
- Transcript for Lecture 24: Modal Analysis: Orthogonality, Mass Stiffness, Damping Matrix Download
- Transcript for Example: Ballistic pendulum, full lecture Download
- Transcript for Lecture outline and Use of tangential and normal coordinates with an example, full lecture Download
- Transcript for Linearization of a 2-DOF system, full lecture Download
- Transcript for Lecture 6: Torque and the Time Rate of Change of Angular Momentum Download
- Transcript for Two examples using polar coordinates, full lecture Download
- Transcript for Lecture 5: Impulse, Torque, and Angular Momentum for a System of Particles Download
- Transcript for Complete, independent and holonomic, full lecture Download
- Transcript for My personal research area: Flow-induced vibration of long strings and beams in fluid flow, full lecture Download
- Transcript for The importance of inertial reference frames, full lecture Download
- Transcript for Recitation 6: Angular Momentum and Torque Download
- Transcript for Lecture 25: Modal Analysis: Response to IC's and to Harmonic Forces Download
- Transcript for Lecture 16: Kinematic Approach to Finding Generalized Forces Download
- Transcript for Outline of the final three lectures, full lecture Download
- Transcript for Recitation 3: Motion in Moving Reference Frames Download
- Transcript for Problem 6 and 7-more pendula, full lecture Download
- Transcript for Fictitious centrifugal force, full lecture Download
- Transcript for Example 3: Muddy card issue about dh/dt and torques, full lecture Download
- Transcript for Recitation 7: Cart and Pendulum, Direct Method Download
- Transcript for Recitation 2: Velocity and Acceleration in Translating and Rotating Frames Download
- Transcript for Concept question discussion of Problem set 9-keep, full lecture Download
- Transcript for Demonstration of the response of a string to harmonic excitation, full lecture Download
- Transcript for Vibrating string demonstration, full lecture Download
- Transcript for Notation Systems Download
- Transcript for Mode superposition analysis of a 2-DOF system, full lecture Download
- Transcript for Moving frames: translation and rotation, full lecture Download
- Transcript for Finding the modes shapes of the 2 DOF system, full lecture Download
- Transcript for Lecture 10: Equations of Motion, Torque, Angular Momentum of Rigid Bodies Download
- Transcript for Vibration isolation of the source-H-Ft/Fo transferfunction-with strobe light demo, full lecture Download
- Transcript for Derivation of the "wave equation", full lecture Download
- Transcript for Generic pendulum by Lagrange, full lecture Download
- Transcript for Example 1: Rotating mass on a string; dP/dt = tension, full lecture Download
- Transcript for Lecture 3: Motion of Center of Mass; Acceleration in Rotating Ref. Frames Download
- Transcript for Overview of the vibration material to be covered in the course, full lecture Download
- Transcript for Angular momentum for rigid bodies and the mass moment of inertia matrix, [I], full lecture Download
- Transcript for Equivalent forces and moments acting only upon the center of mass, full lecture Download
- Transcript for Lecture 16: Kinematic Approach to Finding Generalized Forces Download
- Transcript for Lecture 14: More Complex Rotational Problems and Their Equations of Motion Download
- Transcript for Kinematics: describing the motion of particles and rigid bodies, full lecture Download
- Transcript for Class 4 example of the pipe rolling on a truck bed, full lecture Download
- Transcript for Kinematics: in translating and rotating frames, full lecture Download
- Transcript for Lecture 11: Mass Moment of Inertia of Rigid Bodies Download
- Transcript for Condensing many forces to one force and one moment at center of mass, full lecture Download
- Transcript for Notation Systems Download
- Transcript for Lecture 24: Modal Analysis: Orthogonality, Mass Stiffness, Damping Matrix Download
- Transcript for Matlab simulation of the response of the 2 DOF system to initial conditions, full lecture Download
- Transcript for Cart and pendulum 2 DOF equations of motion, full lecture Download
- Transcript for The vibration of beams: natural frequencies as a function of boundary conditions, dispersion in wave propagation, full lecture Download
- Transcript for Newton's 3rd law recap and application to rigid bodies, full lecture Download
- Transcript for Rayleigh damping and experimental fitting of damping ratios, full lecture Download
- Transcript for Class 3: Unconstrained motion about center of mass-hockey puck example, full lecture Download
- Transcript for Example 2b-work done equals the change in kinetic energy, full lecture Download
- Transcript for Finding natural frequencies and mode shapes of multi-dof systems, full lecture Download
- Transcript for Free vibration of linear multi-DOF systems-intro to mode superposition, full lecture Download
- Transcript for Lecture 9: Rotating Imbalance Download
- Transcript for A review of Newton's three laws of motion, full lecture Download
- Transcript for Hx/F transfer function by complex number approach, full lecture Download
- Transcript for Muddy card discussion, full lecture Download
- Transcript for Notation Systems Download
- Transcript for Example 1: Finding EOMs and DOFs, full lecture Download
- Transcript for Lecture 25: Modal Analysis: Response to IC's and to Harmonic Forces Download
- Transcript for Natural frequencies and mode shapes of the string under tension-with demonstration, full lecture Download
- Transcript for Steady state linear system response to harmonic input, full lecture Download
- Transcript for Recitation 10: Steady State Dynamics Download
- Transcript for The definition of center of rod, full lecture Download
- Transcript for Steady state response to harmonic excitation by the method of modal analysis, full lecture Download
- Transcript for Example 4: Problem with moving points of constraint, full lecture Download
- Transcript for Lecture 19: Introduction to Mechanical Vibration Download
- Transcript for Introduction to the single degree of freedom (SDOF) system, full lecture Download
- Transcript for Lecture 13: Four Classes of Problems With Rotational Motion Download
- Transcript for Class 2: Fixed axis rotation not through center of mass-pendulum example, full lecture Download
- Transcript for Problem solving with an example of a block on a slope, full lecture Download
- Transcript for Finding the equation of motion with respect to the static equilibrium position, full lecture Download
- Transcript for Recitation 11: Double Pendulum System Download
- Transcript for Newton's 3rd Law action and reaction forces, full lecture Download
- Transcript for Recitation 8: Cart and Pendulum, Lagrange Method Download
- Transcript for Review of the concept questions with Homework 10, full lecture Download
- Transcript for Fictitious force: elevator cable breaks, full lecture Download
- Transcript for Lecture 15: Introduction to Lagrange With Examples Download
- Transcript for Fictitious force in the elevator, full lecture Download
- Transcript for Lecture 1: History of Dynamics; Motion in Moving Reference Frames Download
- Transcript for Body on rollers with an internal rotating mass, full lecture Download
- Transcript for Demonstration of a beam with a rotating mass shaker, full lecture Download
- Transcript for Finding the natural frequencies by the characteristic equation, full lecture Download
- Transcript for Concept question discussion-spool and string etc, full lecture Download
- Transcript for Physical demonstration of the motion of a real 2 DOF system, full lecture Download
- Transcript for History of the study of dynamics, full lecture Download
- Transcript for Lecture 7: Degrees of Freedom, Free Body Diagrams, and Fictitious Forces Download
- Transcript for Recitation 7: Cart and Pendulum, Direct Method Download
- Transcript for Lecture 1: History of Dynamics; Motion in Moving Reference Frames Download
- Transcript for Lecture 18: Quiz Review From Optional Problem Set 8 Download
- Transcript for Response to initial conditions using modal analysis, full lecture Download
- Transcript for Estimation of natural frequencies and damping ratios from measured response: the logarithmic decrement, full lecture Download
- Transcript for Kinematic approach to finding generalized forces Example of a wheel on moving cart with an incline, full lecture Download
- Transcript for Problems 2 and 3-Rotating T-bar with imbalance, full lecture Download
- Transcript for Notation Systems Download
- Transcript for Recitation 4: Free Body Diagrams Download
- Transcript for Lecture 4: Movement of a Particle in Circular Motion w/ Polar Coordinates Download
- Transcript for Lecture 18: Quiz Review From Optional Problem Set 8 Download
- Transcript for Predicting natural frequency by SQRT(g/delta), full lecture Download
- Transcript for Lecture 14: More Complex Rotational Problems and Their Equations of Motion Download
- Transcript for Definition of normal and tangential coordinates, full lecture Download
- Transcript for Class 1: Rotation about fixed axis through center of mass, full lecture Download
- Transcript for Example 2: Hockey puck, full lecture Download
- Transcript for Recitation 5: Equations of Motion Download
- Transcript for Discussion of problem set concept questions, full lecture Download
- Transcript for Obtaining uncoupled equations of motion and determination of modal initial conditions, full lecture Download
- Transcript for Demonstration of the response of a string to initial deflection, full lecture Download
- Transcript for Lecture 8: Fictitious Forces and Rotating Mass Download
- Transcript for Lecture 5: Impulse, Torque, and Angular Momentum for a System of Particles Download
- Transcript for Question and answer session, full lecture Download
- Transcript for Lecture 6: Torque and the Time Rate of Change of Angular Momentum Download
- Transcript for Review of applicable physical laws, full lecture Download
- Transcript for Mass sliding on rod example, full lecture Download
- Transcript for Recitation 6: Angular Momentum and Torque Download
- Transcript for Angular momentum of a particle, torque as the time rate of change of angular momentum, and the appearance of the coriolis force, full lecture Download
- Transcript for Recitation 4: Free Body Diagrams Download
- Transcript for Demonstration of modes with the 2 DOF mechanical model, full lecture Download
- Transcript for Parallel axis theorem, full lecture Download
- Transcript for Moments and Products of Inertia, full lecture Download
- Transcript for Lecture 22: Finding Natural Frequencies and Mode Shapes of a 2 DOF System Download
- Transcript for Principle axes and symmetry rules, full lecture Download
- Transcript for Recitation 8: Cart and Pendulum, Lagrange Method Download
- Transcript for Problems 4 and 5-Pendulum in elevator, full lecture Download
- Transcript for Response to initial conditions and the use of Rayleigh damping to model modal damping ratios, full lecture Download
- Transcript for Lecture 12: Problem Solving Methods for Rotating Rigid Bodies Download
- Transcript for Recitation 3: Motion in Moving Reference Frames Download
- Transcript for Lecture 15: Introduction to Lagrange With Examples Download
- Transcript for Purpose of concept questions, full lecture Download
- Transcript for Concept questions intro showing problems, full lecture Download
- Transcript for Example problems, full lecture Download
- Transcript for Questions and answers: discussion of helicopter video and the 300 ton dynamic absorber in the Hancock building, full lecture Download
- Transcript for Lecture 26: Response of 2-DOF Systems by the Use of Transfer Functions Download
- Transcript for Lecture 10: Equations of Motion, Torque, Angular Momentum of Rigid Bodies Download
- Transcript for Review of the use of a transfer function to analyze the response of a single DOF system to harmonic input, full lecture Download
- Transcript for Direct method for assembling the stiffness of an N DOF system, full lecture Download
- Transcript for Lecture 12: Problem Solving Methods for Rotating Rigid Bodies Download
- Transcript for Mass moment of inertia definition as a summation, full lecture Download
- Transcript for Degrees of freedom and free body diagrams, full lecture Download
- Transcript for Lecture 21: Vibration Isolation Download
- Transcript for Lecture 23: Vibration by Mode Superposition Download
- Transcript for Recitation 11: Double Pendulum System Download
- Transcript for Example 4: Rotating mass shaker and effect of gravity on torque, full lecture Download
- Transcript for Lecture 11: Mass Moment of Inertia of Rigid Bodies Download
- Transcript for Demonstration of a vibration isolation system-strobe light and vibrating beam, full lecture Download
- Transcript for Question and answer period, full lecture Download
- Transcript for Lecture 13: Four Classes of Problems With Rotational Motion Download
- Transcript for Lecture 17: Practice Finding EOM Using Lagrange Equations Download
- Transcript for Four classes of rotational problems, full lecture Download
- Transcript for Introduction to kinematics using reference frames and vectors, full lecture Download
- Transcript for Meaning of phase angle in free decay, full lecture Download
- Transcript for Class 4: Rotation about moving points; H/A alternative formulation in terms of H/G, full lecture Download
- Transcript for Reading assignment from Williams on kinematics, full lecture Download
- Transcript for Tipping box problem-alternative form of Eulers equation, full lecture Download
- Transcript for Lecture 17: Practice Finding EOM Using Lagrange Equations Download
- Transcript for Lecture 27: Vibration of Continuous Structures: Strings, Beams, Rods, etc. Download
- Transcript for Lecture 7: Degrees of Freedom, Free Body Diagrams, and Fictitious Forces Download
- Transcript for A review of the principle of linear momentum and impulse, full lecture Download
- Transcript for Recitation 12: Modal Analysis of a Double Pendulum System Download
- Transcript for Lecture 21: Vibration Isolation Download
- Transcript for Application of the wave equation to rods, organ pipes, shower stalls with demonstrations, full lecture Download
- Transcript for Concept question discussion, full lecture Download
- Transcript for Example of the torque/angular momentum relationship to a carnival ride, full lecture Download
- Transcript for Recitation 9: Generalized Forces Download
- Transcript for Example of hockey puck with a pull string-direct method, full lecture Download
13 images
- Photo of a billiards player midway through shooting the cue ball toward the rest of balls, still in… Open ↗
- A male gymnast is in a straddled position midair with his hands reaching down to catch the high bar Open ↗
- Photograph of people on a ride with a round central structure with swings hanging down from it and… Open ↗
- Photograph of a computer screen showing boxes and arrows indicating directions of forces Open ↗
- A man in a red collared shirt and an old-fashioned hat juggles flaming torches Open ↗
- An infant on hands and knees reaches out an exploratory hand toward a large toy spinning top in… Open ↗
- Labeled diagram of a double pendulum Open ↗
- Image of a postage stamp with a portrait of the French mathematician Lagrange Open ↗
- Photo of a large soap bubble on a yellow car with palm trees in the background Open ↗
- Photo of old-fashioned balance scales on a white background Open ↗
- Image of the Brooklyn Bridge taken from on the bridge, looking up Open ↗
- Photographs of ripples in a pond emanating from multiple points Open ↗
- Close up image of piano strings inside a piano Open ↗
Course outline
Newton's Laws, Vectors, and Reference Frames · Lecture Videos
History of the study of dynamics
Newton's Laws, Vectors, and Reference Frames · Lecture Videos
An example deriving equations of motion using Newton's laws
Newton's Laws, Vectors, and Reference Frames · Lecture Videos
Introduction to kinematics using reference frames and vectors
Newton's Laws, Vectors, and Reference Frames · Lecture Videos
Moving frames: translation and rotation
Newton's Laws, Vectors, and Reference Frames · Video
Notation Systems
Newton's Laws, Vectors, and Reference Frames · Video
Lecture 2: Newton's Laws and Describing the Kinematics of Particles
Newton's Laws, Vectors, and Reference Frames · Lecture Videos
Kinematics: describing the motion of particles and rigid bodies
Newton's Laws, Vectors, and Reference Frames · Lecture Videos
A review of Newton's three laws of motion
Newton's Laws, Vectors, and Reference Frames · Lecture Videos
The importance of inertial reference frames
Newton's Laws, Vectors, and Reference Frames · Lecture Videos
Newton's 3rd Law action and reaction forces
Newton's Laws, Vectors, and Reference Frames · Lecture Videos
The definition of center of mass
Newton's Laws, Vectors, and Reference Frames · Lecture Videos
The definition of center of rod
Velocity, Acceleration, and Rotational Motion · Video
Lecture 3: Motion of Center of Mass; Acceleration in Rotating Ref. Frames
Velocity, Acceleration, and Rotational Motion · Lecture Videos
Newton's 3rd law recap and application to rigid bodies
Velocity, Acceleration, and Rotational Motion · Lecture Videos
Kinematics: in translating and rotating frames
Velocity, Acceleration, and Rotational Motion · Lecture Videos
Kinematics: derivative of a rotating vector in cylindrical coordinates
Velocity, Acceleration, and Rotational Motion · Lecture Videos
Lecture 4: Movement of a Particle in Circular Motion w/ Polar Coordinates
Velocity, Acceleration, and Rotational Motion · Lecture Videos
Two examples using polar coordinates
Velocity, Acceleration, and Rotational Motion · Lecture Videos
Angular momentum of a particle, torque as the time rate of change of angular momentum, and the appearance of the coriolis force
Velocity, Acceleration, and Rotational Motion · Lecture Videos
Candy shooter example of coriolis force done in polar coordinates
Velocity, Acceleration, and Rotational Motion · Lecture Videos
Definition of normal and tangential coordinates
Velocity, Acceleration, and Rotational Motion · Problem-solving Videos
Recitation 2: Velocity and Acceleration in Translating and Rotating Frames
Angular Momentum and Torque · Lecture Videos
Lecture 5: Impulse, Torque, and Angular Momentum for a System of Particles
Angular Momentum and Torque · Lecture Videos
A review of the principle of linear momentum and impulse
Angular Momentum and Torque · Lecture Videos
The definition of the angular momentum of a particle with respect to a moving reference point
Angular Momentum and Torque · Lecture Videos
Example of the torque/angular momentum relationship to a carnival ride
Angular Momentum and Torque · Video
Lecture 6: Torque and the Time Rate of Change of Angular Momentum
Angular Momentum and Torque · Lecture Videos
Example 1: Rotating mass on a string; dP/dt = tension
Angular Momentum and Torque · Lecture Videos
Example 2a-Pulling the string from a rotating mass through a hole at the axis of rotation. Conservation of angular momentum, h
Angular Momentum and Torque · Lecture Videos
Example 2b-work done equals the change in kinetic energy
Video unavailable. Open the original course page ↗
Angular Momentum and Torque · Lecture Videos
Example 3b: Computing external and internal structural torques using dh / dt; angular momentum vector not aligned with the axis of rotation
Angular Momentum and Torque · Lecture Videos
Question and answer session
Angular Momentum and Torque · Video
Recitation 3: Motion in Moving Reference Frames
Free Body Diagrams and Fictitious Forces · Lecture Videos
Lecture 7: Degrees of Freedom, Free Body Diagrams, and Fictitious Forces
Free Body Diagrams and Fictitious Forces · Lecture Videos
Degrees of freedom and free body diagrams
Free Body Diagrams and Fictitious Forces · Lecture Videos
Example 2: Hockey puck
Free Body Diagrams and Fictitious Forces · Lecture Videos
Example 3: Rod leaning on a wall
Free Body Diagrams and Fictitious Forces · Lecture Videos
Free body diagrams with two bodies
Free Body Diagrams and Fictitious Forces · Lecture Videos
Fictitious force in the elevator
Free Body Diagrams and Fictitious Forces · Lecture Videos
Fictitious centrifugal force
Free Body Diagrams and Fictitious Forces · Video
Lecture 8: Fictitious Forces and Rotating Mass
Free Body Diagrams and Fictitious Forces · Lecture Videos
Concept questions intro showing problems
Free Body Diagrams and Fictitious Forces · Lecture Videos
Concept question discussion-spool and string etc
Free Body Diagrams and Fictitious Forces · Lecture Videos
Fictitious force: elevator cable breaks
Free Body Diagrams and Fictitious Forces · Lecture Videos
Demo of cart on incline with water in container
Free Body Diagrams and Fictitious Forces · Lecture Videos
Complete fictitious force discussion
Free Body Diagrams and Fictitious Forces · Lecture Videos
Rotating mass demo related to homework 1
Free Body Diagrams and Fictitious Forces · Video
Recitation 4: Free Body Diagrams
Angular Momentum and Rotating Masses · Video
Lecture 9: Rotating Imbalance
Angular Momentum and Rotating Masses · Lecture Videos
Body on rollers with an internal rotating mass
Angular Momentum and Rotating Masses · Lecture Videos
Mass moment of inertia definition as a summation
Angular Momentum and Rotating Masses · Lecture Videos
Moments and Products of Inertia
Angular Momentum and Rotating Masses · Lecture Videos
Lecture 10: Equations of Motion, Torque, Angular Momentum of Rigid Bodies
Angular Momentum and Rotating Masses · Lecture Videos
Example 1: Finding EOMs and DOFs
Angular Momentum and Rotating Masses · Lecture Videos
Example 2: EOM for Atwoods machine
Angular Momentum and Rotating Masses · Lecture Videos
Example 3: Muddy card issue about dh/dt and torques
Angular Momentum and Rotating Masses · Lecture Videos
Example 4: Rotating mass shaker and effect of gravity on torque
Angular Momentum and Rotating Masses · Lecture Videos
Angular momentum for rigid bodies and the mass moment of inertia matrix, [I]
Angular Momentum and Rotating Masses · Problem-solving Videos
Recitation 5: Equations of Motion
Angular Momentum and Motion of Rotating Rigid Bodies · Video
Lecture 11: Mass Moment of Inertia of Rigid Bodies
Angular Momentum and Motion of Rotating Rigid Bodies · Lecture Videos
Principle axes and symmetry rules
Angular Momentum and Motion of Rotating Rigid Bodies · Lecture Videos
Example computation of Izz for a disk
Angular Momentum and Motion of Rotating Rigid Bodies · Lecture Videos
Parallel axis theorem
Angular Momentum and Motion of Rotating Rigid Bodies · Lecture Videos
Lecture 12: Problem Solving Methods for Rotating Rigid Bodies
Angular Momentum and Motion of Rotating Rigid Bodies · Lecture Videos
Class 1: Rotation about fixed axis through center of mass
Angular Momentum and Motion of Rotating Rigid Bodies · Lecture Videos
Class 2: Fixed axis rotation not through center of mass-pendulum example
Angular Momentum and Motion of Rotating Rigid Bodies · Lecture Videos
Class 3: Unconstrained motion about center of mass-hockey puck example
Angular Momentum and Motion of Rotating Rigid Bodies · Lecture Videos
Equivalent forces and moments acting only upon the center of mass
Angular Momentum and Motion of Rotating Rigid Bodies · Lecture Videos
Class 4: Rotation about moving points; H/A alternative formulation in terms of H/G
Angular Momentum and Motion of Rotating Rigid Bodies · Lecture Videos
Class 4 example of the pipe rolling on a truck bed
Angular Momentum and Motion of Rotating Rigid Bodies · Problem-solving Videos
Recitation 6: Angular Momentum and Torque
Finding Equations of Motion for Rigid Body Rotation · Video
Lecture 13: Four Classes of Problems With Rotational Motion
Finding Equations of Motion for Rigid Body Rotation · Lecture Videos
Example 4: Problem with moving points of constraint
Finding Equations of Motion for Rigid Body Rotation · Lecture Videos
Tipping box problem-alternative form of Eulers equation
Finding Equations of Motion for Rigid Body Rotation · Lecture Videos
Question and answer period
Finding Equations of Motion for Rigid Body Rotation · Video
Lecture 14: More Complex Rotational Problems and Their Equations of Motion
Finding Equations of Motion for Rigid Body Rotation · Lecture Videos
Center of percussion problem
Finding Equations of Motion for Rigid Body Rotation · Lecture Videos
Static and dynamic imbalance definitions
Finding Equations of Motion for Rigid Body Rotation · Problem-solving Videos
Recitation 7: Cart and Pendulum, Direct Method
Lagrange Equations · Video
Lecture 15: Introduction to Lagrange With Examples
Lagrange Equations · Lecture Videos
Complete, independent and holonomic
Lagrange Equations · Lecture Videos
Example problems
Lagrange Equations · Problem-solving Videos
Recitation 8: Cart and Pendulum, Lagrange Method
Lagrange Equations Continued · Lecture Videos
Lecture 16: Kinematic Approach to Finding Generalized Forces
Lagrange Equations Continued · Lecture Videos
Kinematic approach to finding generalized forces Example of a wheel on moving cart with an incline
Lagrange Equations Continued · Lecture Videos
Mass sliding on rod example
Lagrange Equations Continued · Video
Lecture 17: Practice Finding EOM Using Lagrange Equations
Lagrange Equations Continued · Lecture Videos
Example of hockey puck with a pull string-direct method
Lagrange Equations Continued · Lecture Videos
Hockey puck by Lagrange
Lagrange Equations Continued · Lecture Videos
Condensing many forces to one force and one moment at center of mass
Lagrange Equations Continued · Lecture Videos
Generic pendulum by Lagrange
Lagrange Equations Continued · Lecture Videos
Examples: Atwood's machine and falling stick
Lagrange Equations Continued · Problem-solving Videos
Recitation 9: Generalized Forces
Quiz Review Lecture & Quiz 2 · Lecture Videos
Lecture 18: Quiz Review From Optional Problem Set 8
Quiz Review Lecture & Quiz 2 · Tutorial Videos
Problems 2 and 3-Rotating T-bar with imbalance
Quiz Review Lecture & Quiz 2 · Tutorial Videos
Problems 4 and 5-Pendulum in elevator
Quiz Review Lecture & Quiz 2 · Tutorial Videos
Problem 6 and 7-more pendula
Mechanical Vibration · Video
Lecture 19: Introduction to Mechanical Vibration
Mechanical Vibration · Lecture Videos
Finding the equation of motion with respect to the static equilibrium position
Mechanical Vibration · Lecture Videos
Response of the SDOF system to initial conditions
Mechanical Vibration · Lecture Videos
Meaning of phase angle in free decay
Mechanical Vibration · Lecture Videos
Engineers approach to the solution of the 2nd order differential equation with initial conditions
Mechanical Vibration · Lecture Videos
Estimation of natural frequencies and damping ratios from measured response: the logarithmic decrement
Mechanical Vibration · Video
Lecture 20: Linear System Modeling a Single Degree of Freedom Oscillator
Mechanical Vibration · Lecture Videos
Damped response of spring-mass-dashpot system to initial conditions
Mechanical Vibration · Lecture Videos
Finding the response of a pendulum to initial conditions
Mechanical Vibration · Lecture Videos
Example: Ballistic pendulum
Mechanical Vibration · Lecture Videos
Experimental determination of damping ratio
Mechanical Vibration · Lecture Videos
Steady state linear system response to harmonic input
Mechanical Vibration · Lecture Videos
Demonstration of a beam with a rotating mass shaker
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Video
Lecture 21: Vibration Isolation
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Demonstration of a vibration isolation system-strobe light and vibrating beam
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Euler's formula for complex numbers
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Hx/F transfer function by complex number approach
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Base motion Hx/y transfer function-vibration isolation system design
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Predicting natural frequency by SQRT(g/delta)
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Vibration isolation of the source-H-Ft/Fo transferfunction-with strobe light demo
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Lecture 22: Finding Natural Frequencies and Mode Shapes of a 2 DOF System
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Finding the natural frequencies by the characteristic equation
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Finding the modes shapes of the 2 DOF system
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Matlab simulation of the response of the 2 DOF system to initial conditions
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Lecture Videos
Physical demonstration of the motion of a real 2 DOF system
Reducing Problem Vibration and Intro to Multi-DOF Vibration · Video
Recitation 10: Steady State Dynamics
Vibration of Multi-Degree-of-Freedom Systems · Video
Lecture 23: Vibration by Mode Superposition
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Overview of the vibration material to be covered in the course
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Linearization of a 2-DOF system
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Free vibration of linear multi-DOF systems-intro to mode superposition
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Finding natural frequencies and mode shapes of multi-dof systems
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Mode superposition analysis of a 2-DOF system
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Lecture 24: Modal Analysis: Orthogonality, Mass Stiffness, Damping Matrix
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Vibrating string demonstration
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Demonstration of modes with the 2 DOF mechanical model
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Orthogonality and the computation of the mass and stiffness matrices
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Response to initial conditions using modal analysis
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Obtaining uncoupled equations of motion and determination of modal initial conditions
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Dealing with damping in modal analysis
Vibration of Multi-Degree-of-Freedom Systems · Lecture Videos
Rayleigh damping and experimental fitting of damping ratios
Vibration of Multi-Degree-of-Freedom Systems · Video
Recitation 11: Double Pendulum System
Vibration Analysis by Mode Superposition · Lecture Videos
Lecture 25: Modal Analysis: Response to IC's and to Harmonic Forces
Vibration Analysis by Mode Superposition · Lecture Videos
Response to initial conditions and the use of Rayleigh damping to model modal damping ratios
Vibration Analysis by Mode Superposition · Lecture Videos
Steady state response to harmonic excitation by the method of modal analysis
Vibration Analysis by Mode Superposition · Lecture Videos
Demonstration of the response of a string to harmonic excitation
Vibration Analysis by Mode Superposition · Lecture Videos
Demonstration of the response of a string to initial deflection
Vibration Analysis by Mode Superposition · Lecture Videos
Direct method for assembling the stiffness of an N DOF system
Vibration Analysis by Mode Superposition · Video
Lecture 26: Response of 2-DOF Systems by the Use of Transfer Functions
Vibration Analysis by Mode Superposition · Lecture Videos
Review of the use of a transfer function to analyze the response of a single DOF system to harmonic input
Video unavailable. Open the original course page ↗
Vibration Analysis by Mode Superposition · Lecture Videos
Analysis of the response of a 2-DOF system to harmonic excitation by means of transfer functions and the introduction of the application of the dynamic absorber to mitigate problem vibration
Vibration Analysis by Mode Superposition · Lecture Videos
Demonstration of a dynamic absorber using a strobe and a vibrating beam
Video unavailable. Open the original course page ↗
Vibration Analysis by Mode Superposition · Lecture Videos
Questions and answers: discussion of helicopter video and the 300 ton dynamic absorber in the Hancock building
Vibration Analysis by Mode Superposition · Lecture Videos
Lecture 27: Vibration of Continuous Structures: Strings, Beams, Rods, etc.
Vibration Analysis by Mode Superposition · Lecture Videos
My personal research area: Flow-induced vibration of long strings and beams in fluid flow
Vibration Analysis by Mode Superposition · Lecture Videos
Derivation of the "wave equation"
Vibration Analysis by Mode Superposition · Lecture Videos
Natural frequencies and mode shapes of the string under tension-with demonstration
Vibration Analysis by Mode Superposition · Lecture Videos
Application of the wave equation to rods, organ pipes, shower stalls with demonstrations
Vibration Analysis by Mode Superposition · Lecture Videos
The vibration of beams: natural frequencies as a function of boundary conditions, dispersion in wave propagation
Vibration Analysis by Mode Superposition · Video
Recitation 12: Modal Analysis of a Double Pendulum System
MIT OpenCourseWare, Prof. J. Kim Vandiver, Prof. David Gossard, 2.003SC Engineering Dynamics, Fall 2011.
License: CC BY-NC-SA 4.0 · Edition: Fall 2011 · Open the original course on OCW ↗
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