Dynamics of Particles 01. Introduction to Dynamics

`1. An Overview

💟Mechanics(역학) : The study of how bodies react to forces acting on them.
i. Statics The study of bodies at equilibrium.
ii. Dynamics Physics + Calculus, The basic principle of Dynanmics is Newton's Law, F=ma.

Dynamics
Dealing with the motion of bodies under the action of forces. It has two distinct parts, kinematics and kinetics.
i. Kinematics : the study of motion without reference to the forces which cause motion. Concerned with the geometric aspects of motion. (e.g. position, velocity, accelelation)
ii. Kinetics : relates the action of forced on bodies to their resulting motions. Concerned with the forces causing the motion. 움직임의 원인(힘)을 고려함.

2. Basic Concepts

i. Space

The geometric region occupied by bodies. Position in space is determined relative to some geometric reference system by means of linear and angular measurements.
The primary inertial system(관성 좌표계) : The basic frame of reference for the laws of Newtonian mechanics. This reference system may be considered "fixed" in space.

ii. Time

A measure of the succession of events. It is considered an absolute quantity in Newtonian mechanics.

iii. Mass

The quantitative measure of the inertia or resistance to change in morion of a body. It also considered as the quantity of matter in a body as well as the property which gives rise to gravitational attraction.

iv. Force

The vector action of one body on another.

v. Types of Mechanical Bodies

Particles(질점) : A body of negligible dimensions. Particles have mass and no size.
Rigid body(강체) : A body whose changes in shapre are negligible compared with the overall dimensions of the body or with the changes in position of the body as a whole. Rigid Bodies have mass, size and shape.

3. Newton's Las

The 1st law
A particle remains at rest or continues to move with uniform velocity if there no unbalanced force acting on it.

The 2nd law
$F =ma$
The acceleration of a particle is propotional to the resultant force,$F$ acting on it and is in the direction of this force.

The 3rd law
The forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear.

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Newton's first law is a consequence of the second law since there is no acceleration when the force is zero, and so the particle is either ar rest or is moving with constant velocity.

4. Gravitation, the mutual attraction between bodies.

$F = G\frac{m_1m_2}{r^2}$,

where
$F$ = the mutual force of attraction between two particles,
$G =$ a universal constant called the constant of gravitation $\neq$ gravitational constant($g$)
$m_1, m_2=$ the masses of the two particles.
$r=$ the distance between the centers of the particles.

Effect of a Rotating Earth
The acceleration of a freely falling body as measured from a position attached to the surface of the earth is slightly less than the absolute vale, because the earthe rotates.