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2024　Fundamentals of Mechanics 2 C

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Academic unit or major
Basic science and technology courses
Instructor(s)
Hirahara Toru 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Tue1-2(M-123(H111))  
Group
C
Course number
LAS.P102
Credits
1
Academic year
2024
Offered quarter
2Q
Syllabus updated
2024/3/14
Lecture notes updated
-
Language used
Japanese
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Course description and aims

Following Fundamentals of Mechanics 1, this course teaches the mechanics of systems of interacting particles and rigid bodies (defined as systems of particles in which the distances between particles is fixed) as well as particle motion observed in a coordinate system undergoing acceleration.

Mechanics is important for understanding nature, and is essential for the study of science, engineering, life sciences, and other specialized courses. Building on the mechanics of single particles, students will learn the mechanics of systems of interacting particles. From this, they will learn the motion and balance of rigid bodies. In addition, they will learn particle motion in coordinate systems undergoing accelerated motion as well as inertial forces. At the end of class, students will be able to solve general problems in mechanics.

Thermodynamics, waves, and energy utilization are also key topics that will be covered in this course.

Student learning outcomes

By completing this course, students will be able to:
1) Correctly understand the concepts of momentum, angular momentum, energy, etc. in systems of particles; the center of mass, moment of inertia, etc. in rigid bodies; and mathematically describe them.
2) Correctly understand motion and equilibrium of rigid bodies, and solve actual physical problems by applying the appropriate mathematical formulas.
3) Correctly understand the concept of inertial forces (Coliolis force and centrifugal force) and mathematically describe them.
4) Correctly understand oscillatory and wave motion, and mathematically describe them.
5) Find mathematical solutions to problems in mechanics, expressed by the appropriate equations, and explain the physical meaning of said solutions.

Keywords

relative coordinates, reduced mass, center of mass, momentum, angular momentum, energy, rigid bodies, equilibrium, moment of inertia, inertial force, Coriolis force, centrifugal force, thermodynamics, waves

Competencies that will be developed

Specialist skills ✔ Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Two-thirds of each class is devoted to fundamentals and the rest to advanced content or application. To allow students to get a good grasp of the course contents and practice problem solving skills, problems related to the contents of this course are provided in Exercises in Physics I.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Central force (attraction, repulsion), potential created by sphere. Show that the potential created by a sphere formed by a collection of masse points is the same as if all masses were concentrated at a single center of gravity.
Class 2 Motion and angular momentum of a mass system (center of mass, momentum conservation law, angular momentum conservation law). Explain the laws of conservation of momentum and angular momentum of a mass system.
Class 3 Motion of rigid bodies (conditions of balance, rotation of rigid bodies, moment of inertia). Explain the equations describing the motion of a rigid body and the conditions for rigid body balance.
Class 4 Applications of rigid body motion. Find moments of inertia and conservation laws of angular momentum in familiar objects of daily life and explain their behavior qualitatively.
Class 5 Fundamentals of relative motion (inertial force, center of gravity system, laboratory system, rotating coordinate system, Coriolis force, Foucault force). Explain the relationship between Coriolis force and centrifugal force.
Class 6 Applications of Relative Motion (Explaining various human-made and natural phenomena using relative motion). Calculate the example of the relative motion observed in daily life and check if it agrees with the observed phenomena.
Class 7 Summary and Example Collection. Think of your own example problem, apply what you have learned, and calculate it.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

"Classical Mechanics"　Morikazu Toda, Iwanami-shoten

Reference books, course materials, etc.

"Classical Mechanics"　Shigeru Shinomoto, Hidetsugu Sakaguchi, Tokyo-tosho

Assessment criteria and methods

Learning achievement is evaluated by a final exam.

Related courses

  • LAS.P105 ： Exercises in Physics I

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites.

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