Dynamics

The following are notes from Dynamics, taught at Madison College in Spring 2021 by Archie Paulson.

Note:

• Chapter and section numbers correspond to the textbook Dynamics, 14th ed by R.C. Hibbeler.
• The problem solving videos are served by Blackboard – you will have to be logged in to Madison College Blackboard to access them. These videos were created by the book’s publisher Pearson.
• The example problems include a link to the web document and the Jupyter Notebook (ipynb) so you can use the code.
  • For more on using the Jupyter Notebook, see the resources below.
  • You may download these files but to see the images you will also need to download all the images and place them in a folder called images.

Contents:

• Ch 12: Kinematics of a Particle
• Ch 13: Kinetics of a Particle: Force and Acceleration
• Ch 14: Kinetics of a Particle: Work and Energy
• Ch 15: Kinetics of a Particle: Impulse and Momentum
• Ch 16: Planar Kinematics of a Rigid Body
• Ch 17: Planar Kinetics of a Rigid Body: Force and Acceleration
• Ch 18: Planar Kinetics of a Rigid Body: Work and Energy
• Ch 19: Planar Kinetics of a Rigid Body: Impulse and Momentum
• Ch 20: Three-Dimensional Kinematics of a Rigid Body
• Ch 21: Three-Dimensional Kinetics of a Rigid Body
• Ch 22: Vibrations
• Other resources

Ch 12: Kinematics of a Particle

• chapter sections
  • 12.1 Introduction
  • 12.2 Rectilinear Kinematics: Continuous Motion
  • 12.3 Rectilinear Kinematics: Erratic Motion
  • 12.4 General Curvilinear Motion
  • 12.5 Curvilinear Motion: Rectangular Components
  • 12.6 Motion of a Projectile
  • 12.7 Curvilinear Motion: Normal and Tangential Components
  • 12.8 Curvilinear Motion: Cylindrical Components
  • 12.9 Absolute Dependent Motion Analysis of Two Particles
  • 12.10 Relative-Motion of Two Particles Using Translating Axes
• lecture videos
  • lecture video 12 1-3 (8 min), slides – refers to Kinematic Problem Solving tips page
  • lecture video 12 4-5 (12 min), slides
  • lecture video 12 6-7 (9 min), slides
  • lecture video 12 8 (19 min), slides
  • lecture video 12 9-10 (8 min), slides
• problem solving videos
  • you must be logged into Blackbaoard to see these videos
  • Particle Kinematics – Kinematics with Multiple Particles – Rectilinear Kinematics of a Particle – General Curvilinear Motion of a Particle – Velocity Kinematics of a Projectile – Normal and Tangential Acceleration – Particle Kinematics Along a Helix – Cylindrical Components of Particle Motion – Velocity Kinematics of a Pulley System – Relative Velocity and Acceleration
• example problems from the text
  • Ch 12 problems – ch12-problems.ipynb

Ch 13: Kinetics of a Particle: Force and Acceleration

• chapter sections
  • 13.1 Newton’s Second Law of Motion
  • 13.2 The Equation of Motion
  • 13.3 Equation of Motion for a System of Particles
  • 13.4 Equations of Motion: Rectangular Coordinates
  • 13.5 Equations of Motion: Normal and Tangential Coordinates
  • 13.6 Equations of Motion: Cylindrical Coordinates
• lecture videos
  • lecture video 13 1-4 (14 min), slides – example problem 13 1-4 (13 min)
  • lecture video 13 5 (6 min), slides
  • lecture video 13 6 (9 min), slides – 13-6 problem (24 min), written work
• problem solving videos
  • you must be logged into Blackbaoard to see these videos
  • Particle Kinetics and Kinematics – Particle Kinetics with a Pulley – Particle Kinetics with Friction – Multi-Particle Kinetics – Particle Kinetics-Normal-Tangential Components – Particle Kinetics-Cylindrical Coordinates
• example problems from the text
  • Ch 13 problems – ch13-problems.ipynb

Ch 14: Kinetics of a Particle: Work and Energy

• chapter sections
  • 14.1 The Work of a Force
  • 14.2 Principle of Work and Energy
  • 14.3 Principle of Work and Energy for a System of Particles
  • 14.4 Power and Efficiency
  • 14.5 Conservative Forces and Potential Energy
  • 14.6 Conservation of Energy
• lecture videos
  • lecture video 14 1-2 (13 min), slides
  • lecture video 14 3-4 (9 min), slides
  • lecture video 14 5-6 (15 min), slides
• problem solving videos
  • you must be logged into Blackbaoard to see these videos
  • Work-Energy Relationship – Work-Energy-Work Due to Friction – Work-Energy and Particle Kinematics – Power and Motor Efficiency – Work-Energy-Potential Energy of a Spring – Conservation of Energy and Particle Kinetics
• example problems from the text
  • Ch 14 problems – ch14-problems.ipynb

Ch 15: Kinetics of a Particle: Impulse and Momentum

• chapter sections
  • 15.1 Principle of Linear Impulse and Momentum
  • 15.2 Principle of Linear Impulse and Momentum for a System of Particles
  • 15.3 Conservation of Linear Momentum for a System of Particles
  • 15.4 Impact
  • 15.5 Angular Momentum
  • 15.6 Relation Between Moment of a Force and Angular Momentum
  • 15.7 Principle of Angular Impulse and Momentum
  • 15.8 Steady Flow of a Fluid Stream
  • 15.9 Propulsion with Variable Mass
• lecture videos
  • lecture video 15 1-2 (10 min), slides – Supplementary: collision simulation
  • lecture video 15 3-4 (17 min), slides
  • lecture video 15 5-6 (8 min), slides – example problem 15 5 (7 min) (jupyter notebook examples)
  • lecture video 15-7 (8 min), slides
  • lecture video 15-8 (14 min), slides
  • lecture video 15-9 (17 min), slides
• Supplementary: flow simulation
• problem solving videos
  • you must be logged into Blackbaoard to see these videos
  • Linear Impulse and Momentum – Linear Impulse Over Finite Time Interval – Conservation of Linear Momentum – Impact of a Bouncing Ball – Angular Momentum of a Particle – Conservation of Angular Momentum – Steady Fluid Stream
• example problems from the text
  • Ch 15 problems – ch15-problems.ipynb

Ch 16: Planar Kinematics of a Rigid Body

• chapter sections
  • 16.1 Planar Rigid-Body Motion
  • 16.2 Translation
  • 16.3 Rotation about a Fixed Axis
  • 16.4 Absolute Motion Analysis
  • 16.5 Relative-Motion Analysis: Velocity
  • 16.6 Instantaneous Center of Zero Velocity
  • 16.7 Relative-Motion Analysis: Acceleration
  • 16.8 Relative-Motion Analysis using Rotating Axes
• lecture videos
  • lecture video 16-1-3 (16 min), slides
  • lecture video for cross product review (10 min), slides
  • (No video lecture for section 16.4), slides
  • lecture video 16-5 (14 min), slides
  • lecture video 16-6 (11 min), slides
  • lecture video 16-7 (10 min), slides
  • lecture video 16-8 (21 min), slides
• problem solving videos
  • you must be logged into Blackbaoard to see these videos
  • Rigid Body Kinematics – Fixed Axis Rotation Gear Kinematics – Fixed Axis Rotation Pully Kinematics – Kinematics of a Scotch Yoke – Relative Velocity in a Piston Mechanism – Velocity Analysis Using Instant Centers – Relative Acceleration Analysis – Relative Acceleration-Rotating Coordinates
• example problems from the text
  • Ch 16 problems – ch16-problems.ipynb

Ch 17: Planar Kinetics of a Rigid Body: Force and Acceleration

• chapter sections
  • 17.1 Mass Moment of Inertia
  • 17.2 Planar Kinetic Equations of Motion
  • 17.3 Equations of Motion: Translation
  • 17.4 Equations of Motion: Rotation about a Fixed Axis
  • 17.5 Equations of Motion: General Plane Motion
• lecture videos
  • lecture video 17-1 (16 min), slides
  • lecture video 17-2-5 (26 min), slides – example: bar slips down wall (33 min) (see jupyter notebook examples)
• problem solving videos
  • you must be logged into Blackbaoard to see these videos
  • Moment of Inertia-Composite Body – Moment of Inertia – Planar Kinetics-Dynamic Slip-Tip – Translational Kinetics – Rotational Kinetics – General Planar Kinetics
• example problems from the text
  • Ch 17 problems – ch17-problems.ipynb

Ch 18: Planar Kinetics of a Rigid Body: Work and Energy

• chapter sections
  • 18.1 Kinetic Energy
  • 18.2 The Work of a Force
  • 18.3 The Work of a Couple Moment
  • 18.4 Principle of Work and Energy
  • 18.5 Conservation of Energy
• lecture videos
  • lecture video 18-1-4 (6 min), slides
  • lecture video 18-5 (4 min), slides
• problem solving videos
  • you must be logged into Blackbaoard to see these videos
  • Work-Energy of a Rolling Ball – Work of a Couple Moment – Work of a Spring – Work of Gravity – Conservation of Energy
• example problems from the text
  • Ch 18 problems – ch18-problems.ipynb

Ch 19: Planar Kinetics of a Rigid Body: Impulse and Momentum

• chapter sections
  • 19.1 Linear and Angular Momentum
  • 19.2 Principle of Impulse and Momentum
  • 19.3 Conservation of Momentum
• lecture videos
  • lecture video 19-1-2 (7 min), slides
  • (no lecture video), slides
• problem solving videos
  • you must be logged into Blackbaoard to see these videos
  • Gravitational Impulse – Momentum of a Rolling Spool – Conservation of Momentum
• example problems from the text
  • Ch 19 problems – ch19-problems.ipynb

Ch 20: Three-Dimensional Kinematics of a Rigid Body

• chapter sections
  • 20.1 Rotation About a Fixed Point
  • 20.2 The Time Derivative of a Vector Measured from Either a Fixed or Translating-Rotating System *
  • 20.3 General Motion
  • 20.4 Relative-Motion Analysis Using Translating and Rotating Axes *
• lecture videos
  • lecture video 20-1-2-3 (34 min), slides
  • lecture video 20-4 (9 min), slides
• problem solving videos
  • you must be logged into Blackbaoard to see these videos
  • General Three-Dimensional Kinematics – Three-Dimensional Kinematics-Rolling – Three-Dimensional Kinematics-Sliding – Three-Dimensional Kinematics in a Rotating Frame
• example problems from the text
  • Ch 20 problems – ch20-problems.ipynb

Ch 21: Three-Dimensional Kinetics of a Rigid Body

• chapter sections
  • 21.1 Moments and Products of Inertia
  • 21.2 Angular Momentum
  • 21.3 Kinetic Energy
  • 21.4 Equations of Motion *
  • 21.5 Gyroscopic Motion *
  • 21.6 Torque-Free Motion
• lecture videos
  • lecture slides 21-1, notes (pdf)
  • lecture slides 21-2-3, notes (pdf)
• problem solving videos:
  • you must be logged into Blackbaoard to see these videos
  • Mass Moment of Inertia – 3D Kinetics Impulse – 3D Kinetics Momentum
• example problems from the text
  • Ch 21 problems – ch21-problems.ipynb

Ch 22: Vibrations

• chapter sections
  • 22.1 Undamped Free Vibration *
  • 22.2 Energy Methods *
  • 22.3 Undamped Forced Vibration *
  • 22.4 Viscous Damped Free Vibration *
  • 22.5 Viscous Damped Forced Vibration *
  • 22.6 Electrical Circuit Analogs *
• problem solving videos:
  • you must be logged into Blackbaoard to see these videos
  • Natural Period of a System – Vibrations with Energy Methods – Undamped Forced Vibration – Damped Free Vibration – Damped Forced Vibration – Electrical System Vibration Analogy

(sections with a * are often skipped)

Other resources

• Reference pages
  • Equation Sheet (pdf)
  • Kinematic Problem Solving
  • From the Pearson Dynamics textbook
    • Equations from textbook cover (pdf) – including geometric tables
    • Mathematical Expressions (pdf) – Appendix A from text
    • Study Pack (pdf) – A 168 page document created by Pearson (the textbook publisher) with Section Summaries, Review Questions and Answers, and a Free-Body Diagram Workbook
• Jupyter Notebook - a scientific computing environment
  • Archie’s IPython Intro for the idea.
  • How to get started to run your own.
  • Problem examples in ipy for demonstration. (ipynb file)
  • Note all the example problems above have an associated Jupyter Notebook (ipynb) files.
• Other calculators and computing resources
  • Desmos is a nice free graphing calculator
  • Wolfram Alpha can do equation solving and calculus
• University Physics textbook – Dynamics covers the material from chapters 3-11 in this textbook.
• Other video resources:
  • Jeff Hanson’s Online Dynamics Course on youtube. He breaks down all the important topics at a white board and does several example problems.
• Problem Solving Tips:
  • Read the Directions – Many mistakes on homework and exams are made because students fail to read the instructions. This can be particularly detrimental on exams if unnecessary work is performed that wastes valuable time.
  • Work Symbolically – It is often preferable to develop solutions in terms of symbols instead of numbers: symbolic problem solving notes (pdf).
• Sample exams (pdfs)
  • exam 1 – Ch 12 & 13 – solutions
  • exam 2 – Ch 14 & 15 – solutions
  • exam 3 – Ch 16 & 17 – solutions
  • final exam – Ch 12-20 – solutions
• Having your own copy of the textbook is a good idea if you plan to continue in engineering, as it will become a valuable resource for you in the future. You may find used textbooks fairly cheap from various vendors online (such as Chegg.com of GetTextbooks.com) or by web search.

Last modified: January 2024 by Archie.