Introduction to mechanics

Mechanics:-

So, what is mechanics? Mechanics we can say is an exact science. Again the question is what do I mean by an exact science. When we say that the physics or any branch of it is an exact science by this we mean that , its laws are expressed in the from of mathematical equations which describe and predict the results of precise quantitative measurements.

Mechanics is the study of the motions of material bodies. It may be further subdivided into three sub disciplines namely,

1. Kinematics :- Study and description of the possible motions of material bodies.
2. Dynamics :- It is the study of the laws which determine , among all possible motions, which motion will actually take place in in any given case.
3. Statics :- It is the study of forces and system of forces, with particular reference to system of forces which act on bodies at rest.

Every motion whether it is linear or rotational is governed by certain laws. Mechanics deals with these laws and formulates them in a scientific manner so that we can predict results. The concept of ‘force’ is fully explained by Newton through his laws of motion. The basic ideas of state of rest and uniform motion were studied by various philosophers. According to Aristotle (384 – 322 BC), a constant force has to be applied on a body so as to keep it in motion with constant velocity. Later on, Galileo (1564 – 1642 AD) stated that no force is required for a body to move with uniform velocity. Newton (1642 – 1727) was the first person who formulated the laws differentiating ‘state of rest’ and ‘state of uniform motion’.

Note:-  Symbols which appear in the equations that express the laws of science should represent quantities which can be expressed in numerical terms.

SOME IMPORTANT TERMS

To understand the motion of a body in different Frame of reference we came across few terms like

1. Particle:- It is just a quantity of matter,  having practically no linear dimensions but possesses only a position; the measure of this quantity of matter being the mass of the particle.
2.  Event:- An event stands for anything that occurs suddenly or instantaneously at a point in space. It, thus, involves both, a position and time of occurrence.
3. Observer:- A person or an equipment that can locate, record, measure and interpret an event is called an observer.

NEWTON’S NOTIONS OF SPACE

In Newton’s model both space and time are unaffected by the presence or absence of objects. That is space and time are absolute, an arena where the play of Nature unfolds. In Newton’s words,

Absolute space in its own nature, without relation to anything external, remains always similar and immovable.

1. Space is three dimensional :- The concept of space and time is fundamental to the study of mechanics. All objects occupy space and have length, breadth and height. Space is, therefore, three dimensional. This is why the position of a point can be specified completely by the three co-ordinates (x, y, z) or $(r, \theta, \phi)$.
2.  Space is flat :- i.e., it possesses Euclidean flatness. This means that the shortest distance between any two points in space is a straight line. If we take three points in space to form a triangle, the sum of angles is equal  to $\pi$. If it is a right angled triangle, then the three sides are related by Pythagoras Theorem i.e., Hypotenuse2 = Base
2 + Altitude2 However, according to latest theory, space is not exactly flat but somewhat curved. The departure from flatness is very small and can be ignored in the study of classical mechanics.
3. Space is homogeneous:- In other words, space is everywhere alike. Homogeneity of free space (a space in which fields and forces are absent) means transnational invariance of its properties i.e., the result of an experiment is not altered due to linear displacement of the co-ordinate systems.
4. Space is isotropic :- It means that if we consider a point O in space and we move from this point in any direction, the properties are the same i.e., there is nothing to distinguish one direction from the other. In other words, there is no preferred direction in space or one direction is as good as any other direction.