Following Fundamentals of Mechanics 1, this course teaches particle motion observed in a coordinate system undergoing acceleration as well as the mechanics of systems of interacting particles and rigid bodies (defined as systems of particles in which the distances between particles is fixed).
Mechanics is important for understanding nature, and is essential for the study of science, engineering, life sciences, and other specialized courses. On the basis of the mechanics of single particle, students will learn particle motion in coordinate systems undergoing accelerated motion as well as inertial forces. Moreover, students will learn the mechanics of systems of interacting particles, as well as the motion and balance of rigid bodies. From this, students will be able to solve general problems in mechanics.
By completing this course, students will be able to:
1) Understand the concepts of inertial forces (Coriolis force and centrifugal force) correctly, and describe them mathematically.
2) Understand the concepts of momentum, angular momentum, energy, etc. in systems of particles and the center of mass, moment of inertia, etc. in rigid bodies, correctly, and describe them mathematically.
3) Understand motion and equilibrium of rigid bodies correctly, and solve actual mechanical problems by applying the appropriate mathematical formulas.
4) Find mathematical solutions to problems in mechanics, expressed by the appropriate equations, and explain the physical meaning of said solutions.
coordinate transform, inertial force, Coriolis force, centrifugal force, relative coordinates, reduced mass, center of mass, momentum, angular momentum, energy, rigid body, equilibrium, moment of inertia
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Two-thirds of each class are devoted to fundamentals and the rest to advanced content or application. To allow students to get a good understanding of the course contents and practice application, problems related to the contents of this course are provided in Exercises in Physics I.
Course schedule | Required learning | |
---|---|---|
Class 1 | Motion of two interacting particles (relative coordinates, reduced mass) | Understanding 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) | Understanding 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 varioius 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 | Be able to compare and contrast the Coriolis force with the centrifugal force. |
Class 8 | Thermodynamics, waves, and energy utilization | Understanding the basics of the Carnot cycle and the one-dimensional wave equation. |
Toda Morikazu. Rikigaku (Mechanics). Iwanami Shoten; ISBN-13: 978-4000076418. (Japanese)
Unspecified.
Learning achievement is evaluated by a final exam.
No prerequisites.