# Mechanics I

Lecturer Takayoshi OHSHIMA, Professor Institute of Liberal Arts & Sciences, 2003 Spring Science freshmen (2・1.5 Hrs. / session 1 session / week 15 weeks / semester)

### Course Home

Main objective of this course is to learn about mechanics by looking into the daily events from mechanical point of view. Since mechanics are the fundamental subject for learning natural sciences, this course is designed not only for the students who would like to pursue their research on physics in the future but also for all the natural science major students. The material covered in this class will be continued to Mechanics 2, which will be open in the 2nd semester. These two courses will cover the basics of Newtonian dynamics.

### Key Features

Mechanics is underlying concept of any field of physics. Therefore it is important to fully understand the materials taught in this lecture. It is widely believed that setting up the equation of motion is the main goal of mechanics. However I would like to emphasize on visualizing the motion of the body in your head when solving the problems because this practice will enable you to understand concept of mechanics deeply. Therefore, in this class we will focus on the daily events and compare what you observe with the result you have obtained from the equation of motion. More advanced self-learning materials are provided for those who would like to study further.

High school-level of physics is necessary for this class. If you have no experience in studying physics, it is highly recommended that you prepare and review for the lecture so as to get the better understanding of the basics.

### Contents

(1) Mathematical preliminary

• Introduction of basic concepts and mathematical contents.
• Position, velocity and acceleration.
• Vector, calculus and differential equation.

(2) Equation of motion

• Newton's Laws of motion and its application for simple case.
• Example problems on the motion of raindrop under the influence of gravity with the upward force of air resistant.
• Equation of motion of the simple pendulum and spring, and its characteristics of the solution.

(3) Conservative force and potential

• Introduction of momentum, angular momentum and energy.
• Conservation of energy and its relation to work, potential and conservative force.
• Concept of field and potential.

(4) Vibration and wave

• Forced vibration, damped vibration and coupled vibration.
• Example problem on automatic door and earthquake.
• Solution of wave equation and its application.
• Example problem on ripple in a river, wave propagating on string and acoustic wave.

(5) Coordinate conversion and inertia force

• Inertia system, Galilean transformation, inertia force and rotating coordinate system.
• Coriolis force and its relation to the rotating coordinate system.
• Example problem on why typhoon is rotating sinisterly.
• Foucault pendulum and tidal force.

### Course Schedule

Session Contents
1 - Introduction: Attitude toward learning natural sciences
2 - Equation of motion
- Vector, velocity, and acceleration
3 - Unit systems
- Parabolic motion
4 - Motion of body when resistance force is give as a function of velocity
5 - Falling motion of an ant
6 - Circular motion
7 - Simple pendulum
- Integration of equation of motion
8 - Conservative force and potential
9 - Example problem on universal gravitation - Harmonic oscillation
10 - Damped vibration
11 - Forced vibration
- Coupled vibration
12 - Wave
13 - Inertia force
- Rotating coordinate system
14 - Foucault pendulum
15 -Summary
- End-of-term examination

### Lecture Handouts

Lecture note is not provided since it is better for student to take note in class.

This is the reference material for the lecture.

Since there are lots of excellent textbooks, these materials uploaded here are intended to increase your interest in physics.

No.2

No.3

No.4

No.5

No.6

No.7

No.8

No.9

No.10

No.11

No.12

No.13

No.14

Grading will be based on attendance, assignment papers, mid term examination and end-of-term examination.

### Related Resources

A. P. French, Newtonian Mechanics (M.I.T. Introductory Physics Series), W. W. Norton Publishing, 1st edition (1971)
A Japanese version of this book is also available.

#### Last updated

May 19, 2020

OCW website, and all course materials made public on this site,
may be used under the terms and conditions posted under "About OCW"
© 2020 Nagoya University Open Course Ware