This page provides a set of links to notes, equation sheets, example problems, and recommended exercises in elementary dynamics (often referred to as engineering mechanics – dynamics). The topics covered are those typically covered in a first course in two-dimensional dynamics in engineering curricula.
Right: Free-Body Diagram
Reference: R. C. Hibbeler, Engineering Mechanics: Dynamics, 13th Edition, Prentice-Hall, 2013.
Problem Solving
Notes
Particle Motion:
- Rectilinear Motion
- Acceleration Profiles
- Acceleration Profiles Example
- Curvilinear Motion – Rectangular Components
- Curvilinear Motion – Normal and Tangential Components
- Curvilinear Motion – Radial and Transverse Components
- Dependent Motion: Pulley Problems
- Relative Motion of Two Particles
- Kinetics of Particles: Newton’s Second Law
- Kinetics of Particles: Principle of Work and Energy
- Kinetics of Particles: Power and Efficiency
- Kinetics of Particles: Conservation of Energy
- Kinetics of Particles: Principle of Impulse and Momentum
- Kinetics of Particles: Conservation of Linear Momentum
- Kinetics of Particles: Impact
Rigid Body Motion:
- Introduction to Rigid Body Kinematics in Two Dimensions
- Rotational Motion about a Fixed Axis
- Relative Velocity of Two Points Fixed on a Rigid Body
- Instantaneous Centers of Zero Velocity
- Relative Acceleration of Two Points Fixed on a Rigid Body
- Point Moving on a Rigid Body (Sliding Contact)
- Center of Mass in Two Dimensions
- Mass Moments of Inertia in Two Dimensions
- Angular Momentum of a Rigid Body in Two Dimensions
- Newton’s Law for Rigid Body Motion in Two Dimensions
- Work and Energy Principles for Rigid Body Motion in Two Dimensions
- Principle of Impulse and Momentum for Rigid Body Motion in Two Dimensions
- Conservation of Momentum and Impact for Rigid Bodies in Two Dimensions
- Introduction to Vibrations
Equation Sheets
Example Problems
- 01 – Rectilinear Motion Example #1
- 02 – Rectilinear Motion Example #2
- 03 – Rectilinear Motion Example #3
- 04 – 2D Motion Using Rectangular Components Example #1
- 05 – 2D Motion Using Rectangular Components Example #2
- 06 – 2D Motion Using Normal & Tangential Components Example #1
- 07 – 2D Motion Using Normal & Tangential Components Example #2
- 08 – 2D Motion Using Normal & Tangential Components Example #3
- 09 – 2D Motion Using Radial & Transverse Components Example #1
- 10 – 2D Motion Using Radial & Transverse Components Example #2
- 11 – 2D Motion Using Relative Motion Concept Example #1
- 12 – 2D Motion Using Relative Motion Concept Example #2
- 13 – Particle Newton’s Law Using Rectangular Components Example #1
- 14 – Particle Newton’s Law Using Rectangular Components Example #2
- 15 – Particle Newton’s Law Using Normal & Tangential Components Example #1
- 16 – Particle Newton’s Law Using Normal & Tangential Components Example #2
- 17 – Particle Newton’s Law Using Radial & Transverse Components Example #1
- 18 – Particle Newton’s Law Using Radial & Transverse Components Example #2
- 19 – Particle Work & Energy Example #1
- 20 – Particle Work & Energy Example #2
- 21 – Particle Work & Energy Example #3
- 22 – Particle Conservation of Energy Example
- 23 – Particle Impulse & Momentum Example #1
- 24 – Particle Impulse & Momentum Example #2
- 25 – Particle Conservation of Linear Momentum Example #1
- 26 – Particle Conservation of Linear Momentum Example #2
- 27 – Particle Conservation of Linear Momentum with Impact Example #1
- 28 – Particle Conservation of Linear Momentum with Impact Example #2
- 29 – Rigid Body Kinematics – Pure Rotational Motion Example
- 30 – Rigid Body Kinematics – Relative Velocity Example #1
- 31 – Rigid Body Kinematics – Relative Velocity Example #2
- 32 – Rigid Body Kinematics – Relative Velocity Example #3
32a – Rigid Body Kinematics – Relative Velocity Example #4 - 33 – Rigid Body Kinematics – Instantaneous Centers Example #1
- 34 – Rigid Body Kinematics – Instantaneous Centers Example #2
34a – Rigid Body Kinematics – Instantaneous Centers Example #3
34b – Rigid Body Kinematics – Instantaneous Centers Example #4 - 35 – Rigid Body Kinematics – Relative Acceleration Example #1
- 36 – Rigid Body Kinematics – Relative Acceleration Example #2
- 37 – Rigid Body Kinematics – Relative Acceleration Example #3
- 38a – Rigid Body Kinematics – Sliding Contact Acceleration Example #1
38b – Rigid Body Kinematics – Sliding Contact Acceleration Example #2 - 39 – Rigid Body Kinetics – Mass Center/Inertia Example
- 40 – Rigid Body Kinetics – Translation Example #1
- 41 – Rigid Body Kinetics – Translation Example #2
- 42 – Rigid Body Kinetics – Fixed Axis Rotation Example
- 43 – Rigid Body Kinetics – General Plane Motion Example #1
- 44 – Rigid Body Kinetics – General Plane Motion Example #2
- 45a – Rigid Body Kinetics – Work Energy Example #1
45b – Rigid Body Kinetics – Work Energy Example #2 - 46 – Rigid Body Kinetics – Conservation of Energy Example
- 47 – Rigid Body Kinetics – Impulse & Momentum Example #1
- 48 – Rigid Body Kinetics – Impulse & Momentum Example #2
- 49 – Rigid Body Kinetics – Impulse & Momentum Example #3
- 50 – Rigid Body Kinetics – Impulse & Momentum – Impact Example #1
- 51 – Rigid Body Kinetics – Impulse & Momentum – Impact Example #2
Exercises (all answers provided)
- Exercises #1 – Rectilinear Motion Profiles
- Exercises #2 – Curvilinear Motion: Rectangular Coordinates
- Exercises #3 – Curvilinear Motion: Nonstationary Unit Vectors
- Exercises #4 – Newton’s Laws for Particle Motion
- Exercises #5 – Work, Energy, Energy Conservation, and Newton’s Laws for Particle Motion
- Exercises #6 – Impulse, Momentum, Impact, and Energy for Particle Motion
- Exercises #7 – Two-Dimensional, Rigid Body Kinematics
- Exercises #8 – Two-Dimensional, Rigid Body Kinetics: Inertia and Newton’s Laws
- Exercises #9 – Two-Dimensional, Rigid Body Kinetics: Work & Energy
- Exercises #10 – Two-Dimensional, Rigid Body Kinetics: Impulse, Momentum, and Energy
Dynamics, Motion, and Control 