Engineering Dynamics

Velocity, Acceleration, and Rotational Motion

« Previous | Next »

Session Overview

Covered this week: In week 2, we continue with the study of Newton’s laws. We reviewed the third law and its application to finding the center of mass. Next, we take up the topic of kinematics in translating and rotating frames. In lecture 4, we do a series of examples where velocity and acceleration using polar and cylindrical coordinates, then ending with an introduction to normal and tangential unit vectors. A male gymnast completes a complicated move involving simultaneous rotation and translation. Image courtesy of Singapore 2010 Youth Olympic Games.

Assignments

Problems and Concept Questions

Each problem set has concept questions paired with most problems. Answers to the concept questions are handed in before the overall problem set is due. You should therefore answer the concept questions in each problem set while watching the video lectures for the week. Then, use the Concept Question Answer Key (below in the Check Yourself section) to check your work before continuing to work on the problem set.

Please note that if your answer to the concept question is incorrect, it is likely that you may start down an unproductive pathway to a solution. Try to fully understand the answer to the concept question before you begin the regular problem.

• Problem Set 2: Problems and Concept Questions (PDF)

Suggested Reading

• [Hibbeler] sections sections 12.7, 12.8, 13.5–13.7, 16.7, 16.8.

Videos

Lecture Videos

• Watch Lecture 3: Motion of Center of Mass; Acceleration in Rotating Ref. Frames

  • Chapters
    • Problem solving with an example of a block on a slope
    • Newton’s 3rd law recap and application to rigid bodies
    • Kinematics: in translating and rotating frames
    • Kinematics: derivative of a rotating vector in cylindrical coordinates

• Watch Lecture 4: Movement of a Particle in Circular Motion w/ Polar Coordinates

  • Chapters
    • Vector form of velocity and acceleration in a translating and rotating coordinate system and the expression of them in polar and cylindrical coordinates
    • Two examples using polar coordinates
    • Angular momentum of a particle, torque as the time rate of change of angular momentum, and the appearance of the coriolis force
    • Candy shooter example of coriolis force done in polar coordinates
    • Definition of normal and tangential coordinates

Recitation Video and Notes

• Watch Notation Systems
  • Recitation 2 uses a different notation system than used in Lectures 1 through 4. Please watch this video to see how the two notation systems interrelate.
• Watch Recitation 2: Velocity and Acceleration in Translating and Rotating Frames
  • This recitation includes a concept review for the week and covers an amusement park ride problem with velocity in translating and rotating frames. The class also covers questions regarding planar motion problems.
• Recitation 2 Notes: Planar Motion (PDF - 1.1MB)
  • These recitation notes were compiled by Prof. David Gossard, another instructor for the course. His notes go over concepts and problems covered during the recitation sections he taught, and may not precisely correspond to the content covered in the above recitation video.

Check Yourself

Concept Question Answer Key and Problem Set Solutions

The solutions are presented in two files, one with the answers to the concept questions, and one with solutions and in-depth explanations for the problems. Work the problems on your own and check your answers when you’re done.

• Problem Set 2: Concept Question Answer Key (PDF)
• Problem Set 2: Problem Solutions and Explanations (PDF)

Looking for something specific in this course? The Resource Index compiles links to most course resources in a single page.

« Previous | Next »