This course will provide students with the fundamental knowledge of rigid body (rigid-object) dynamics required to solve mechanical
engineering problems. A real solid object which has a size and particular shape is not point-like particle, and we need to
apply the concepts of the rigid body to a variety of real world engineering problems.
The motion of a rigid body consists of a translation of the center of mass and a rotation about the center of mass. To examine the latter motion, we will introduce the physical quantities associated with rotations: angular momentum, torque and moment of inertia. We then address deriving the relationship between torque and time rate of change of angular momentum. Leaners are expected to be comfortable with philosophy of Newtonian mechanics.
The motion of a rigid body consists of a translation of the center of mass and a rotation about the center of mass. To examine the latter motion, we will introduce the physical quantities associated with rotations: angular momentum, torque and moment of inertia. We then address deriving the relationship between torque and time rate of change of angular momentum. Leaners are expected to be comfortable with philosophy of Newtonian mechanics.
The specific purpose of the class is to develop the ability to use the equation of motion of a rigid body in solving engineering
applications.
- Students will be able to understand the physical meaning of an angular momentum of the object, and to calculate it with respect to any point.
- Students will be able to understand the physical meaning of the conservation law of angular momentum, and to use them to determine a motion of objects.
- Students will be able to understand the physical meaning of a moment of inertia and to calculate the moment of inertia of objects with simple geometry.
- Students will be able to formulate the rotational equation for the rigid-object about a fixed axis, and to determine a planar rotational motion of the rigid-object about the fixed axis.
- Students will be able to formulate the governing equations for the rigid-object motion and to use them to determine a planar motion of the rigid-object.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Description of motion in polar coordinates - Relations between Cartesian and polar coordinates - Velocity and acceleration in polar coordinates (radial and circumferential components) |
- Review the derivatives of composite functions and trigonometric functions | 60minutes |
| - Review the today's lesson by watching lecture video | 60minutes | ||
| 2. | Angular momentum - Definition of the vector product - Properties of the vector product - Definition of the angular momentum of a particle - Physical meaning of the angular momentum |
- Watch the lecture video "Vector product" (15:00) - Watch the lecture video "Definition of the angular momentum vector" (17:00) - Submit the assignment #1 |
90minutes |
| - Review the today's lesson by watching lecture video | 90minutes | ||
| 3. | Conservation law of angular momentum (1) - Relations between torque and rate of change in angular momentum - Conservation of angular momentum |
- Watch the lecture video "Conservation law of angular momentum" (09:17) - Submit the assignment #2 |
90minutes |
| - Review the today's lesson by watching lecture video | 90minutes | ||
| 4. | Conservation law of angular momentum (2) - Exercise in calculation of the angular momentum - Exercise in conservation of angular momentum |
- Submit the assignment #3 | 90minutes |
| - Review the today's lesson by watching lecture video | 90minutes | ||
| 5. | Mid-term examination | - Review the lesson 1-4 | 180minutes |
| - Review the mid-term examination | 90minutes | ||
| 6. | A rigid body rotating about a fixed axis - Angular momentum of the rigid body about a fixed axis - Rotational equation of motion of the rigid body |
- Watch the lecture video "Planar motion of a rigid body" (12:32) - Submit the assignment #4 |
120minutes |
| - Review the today's lesson by watching lecture video | 60minutes | ||
| 7. | Moment of inertia - Definition of the moment of inertia and its physical meaning - Simple moment of inertia calculations for two-dimensional objects (uniform rod, disk) |
- Watch the lecture video "Moment of inertia" (16:49) - Submit the assignment #5 |
90minutes |
| - Review the today's lesson by watching lecture video | 90minutes | ||
| 8. | Exercise in a rigid body rotating about a fixed axis (1) - Dynamics of rigid body planar circular motion - Rotational motion of pulleys |
- Watch the lecture video "A rigid body rotating about a fixed axis" (21:21) - Submit the assignment #6 |
120minutes |
| - Review the today's lesson by watching lecture video | 60minutes | ||
| 9. | Exercise in a rigid body rotating about a fixed axis (2) - A physical pendulum |
- Watch the lecture video "Parallel axis theorem" (17:00) - Submit the assignment #7 |
90minutes |
| - Review the today's lesson by watching lecture video | 90minutes | ||
| 10. | Exercise in a planar motion of a single rigid body (1) - Translational motion of the center of mass - Rotation motion of the center of mass - Fundamental equations of a planar motion of a single rigid body |
- Watch the lecture video "Fundamental equations of a rigid body in planar motion" (08:26) - Submit the assignment #8 |
120minutes |
| - Review the today's lesson by watching lecture video | 60minutes | ||
| 11. | Exercise in a planar motion of a single rigid body (2) - Balance of the rigid body - A planar motion of a single rod |
- Watch the lecture video "Equilibrium conditions of a rigid body" (14:28) - Submit the assignment #9 |
90minutes |
| - Review the today's lesson by watching lecture video | 90minutes | ||
| 12. | Exercise in a planar motion of a single rigid body (3) - Condition of pure rolling - A cylinder rolling down an inclined plane - Motion of a yo-yo |
- Submit the assignment #10 | 120minutes |
| - Review the today's lesson by watching lecture video | 60minutes | ||
| 13. | Exercise in a planar motion of a single rigid body (4) - Rolling and sliding of a disk on horizontal plane - Collision between a particle and a rigid body |
- Submit the assignment #11 | 120minutes |
| - Review the today's lesson by watching lecture video | 60minutes | ||
| 14. | Course summary | - Review the lesson 1-13 | 180minutes |
| - Review the term-end examination | 100minutes | ||
| Total. | - | - | 2650minutes |
| Assignments | Total. | |
|---|---|---|
| 1. | 23% | 23% |
| 2. | 23% | 23% |
| 3. | 14% | 14% |
| 4. | 20% | 20% |
| 5. | 20% | 20% |
| Total. | 100% | - |
Grades will be based on the following items:
• Class activities (quizzes, in-class assignments) and homework assignments : 100 points
You need to earn more than 60 points to pass the course.
If you understand what is written in a textbook and if you can solve questions in a textbook,
you probably can get 60 points in a final score.
• Class activities (quizzes, in-class assignments) and homework assignments : 100 points
You need to earn more than 60 points to pass the course.
If you understand what is written in a textbook and if you can solve questions in a textbook,
you probably can get 60 points in a final score.
Download the course material from following web page:
https://scomb.shibaura-it.ac.jp/
https://scomb.shibaura-it.ac.jp/
Students are expected to be comfortable with the material from the following subjects:
- Fundamentals of Engineering Mechanics 1
- Practice in Engineering Analysis
- Fundamentals of Engineering Mechanics 1
- Practice in Engineering Analysis
- Every Thursday, 16:50-17:50 at Omiya campus
- Non-social and professional independence development course
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Wed Apr 14 04:07:40 JST 2021