### 2021　Fundamentals of Mechanics 2 E

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Basic science and technology courses
Instructor(s)
Uchida Masaki
Class Format
Lecture
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(H101)
Group
E
Course number
LAS.P102
Credits
1
2021
Offered quarter
2Q
Syllabus updated
2021/3/19
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 Motion of two interacting particles (relative coordinates, reduced mass) Explain that the motion of two interacting particles is equivalent to the motion of a single particle.
Class 2 Momentum and angular momentum in a system of particles (center of mass, laws of conservation of momentum and angular momentum) Explain the laws of conservation of momentum and angular momentum for a system of particles.
Class 3 Equations of motion and equilibrium of a rigid body (torque, conditions for equilibirum) Explain the equations of motion for a rigid body and its equilibrium properties.
Class 4 Motion of a rigid body around a fixed axis (moment of inertia, angular momentum and energy of a rigid body, rigid body pendulum) Explain the concept of moment of inertia and how it is used to define the angular momentum and kinetic energy of a rigid body.
Class 5 Calculation of moments of inertia (parallel axis theorem, perpendicular axis theorem) for various rigid bodies Find moments of inertia for various rigid body shapes.
Class 6 Planar motion of a rigid body (rotational motion) Explain rotational motion of a rigid body.
Class 7 Motion in an accelerated coordinate system(inertia force, Coriolis force and centrifugal force) Explain the Coriolis force and the centrifugal force.

### 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)

Morikazu Toda, Mechanics, Iwanami Shoten (Japanese)

None required.

### Assessment criteria and methods

Learning achievement is mainly evaluated by a final exam.

### Related courses

• LAS.P105 ： Exercises in Physics I

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

No prerequisites.