classical mechanics

Addendum to Coriolis Force; Definition of Centripetal Force.

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We need to understand first that Force can be categorized into two types. One is called tangential or collinear force. This component of the force is always along the direction of motion and changes speed of an object. It can change direction once the velocity of the object has become zero. Its NOT centripetal force. It can never make an object go in a plane or 3 D trajectory, as the motion is limited to only one dimension. The object can only go back and forth.

Now look at the other component. Its called a radial force. Its always perpendicular to the direction of motion. This force is called centripetal force, always. Note that its different from what we call central forces.

In consequence, both tangential and radial forces can be central.

Relative velocity is the velocity vector determined from consideration of its value (magnitude and direction) from two different frames of references and relating them.

Solutions to Irodov problems

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Problems In General Physics, 
I.E. Irodov
Part-I Physical Fundamentals in Mechanics.

Chapter 1.1 Kinematics.  

10 interesting problems in elementary mechanics

This post intends to provide 40 interesting problems in elementary mechanics from IE Irodov, Problems in general physics that I solved in last couple weeks. Note that another 30 problems (additional 12 at hand) which has been solved will be uploaded after they are scanned, shortly.

Basic Concepts.
In this class today we will discuss the subject of “kinematics” briefly and solve some problems, based on the same. 

The motion of objects are studied under the heading “mechanics”.

♣ Mechanics is called “kinematics” if we study about the “nature of motion” without regard to what factors are causing such motion. 

♣ In addition to kinematics, when we focus our attention to study the factors that cause motion, such is named as dynamics. 

In kinematics today we will discuss a few problems that will cover the topics of …

Uncertainty Principle Again.

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2. The object can be a large object, eg say something whose picture you are taking. But as explained above its not the energy of the object (or momentum) which is directly coming into the problem. That would be an added degree of concern if the object is moving with certain velocity, a reason why pictures are blurred. Because motion of objects introduces additional energy-time-momentum-position variables and their corresponding uncertainties. For the argument of the above problem one can imagine the large sized object, lets say a bird, is standing still on a tree while its picture is being taken. In that case if the wavelength of the light [few 100 nano meters = 1/10th of a micrometer] is used (eg in a digital-camera) the corresponding accuracy of the light will be less than micrometers. You can take a very sharp picture of the bird, which is lets say 6 inch long. But when you zoom in to a large degree, the inaccuracies will show up. [in this case how to see a micrometer level image? Is a computer sufficient to show us the uncertain edges of the pixels?] If the wavelength (here visible light) is so small, evidently by de-Broglie relationship, momentum or energy of such light is very large. But its not as large to disturb the feelings of the bird. The bird doesn’t have a problem with visible light, and such energy does not disturb its position or energy or any thing so to say. So while Quantum Mechanics is valid, we are accustomed to say this is a classical mechanics situation. To say QM is invalid is incorrect. To say QM is understood to be valid is a knowledgeable position.

Do we have two theories for two different scales of reality?

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Quantum laws pervade everywhere. The diffraction of prism or windows, the little stars that sparkle on your window pane are all quantum mechanical effects brought into the fore of our sight. We gaze at it from our convenience, but they are produced at the minion and carried forth without prejudice to yet another scale, the scale of ours. The electro-magnetic effects from stars that are received by us is an example of how quantum effects have been carried to the grand scale of planets and stars. Classical mechanics would not have explained because they are not produced classically, just like the shoes do not explain bacteria. But bacteria causes bloodshed in our posterior. They came from within not outside demons of bible. Bible explains things that do not exist. But Quantum Mechanical laws explains things that exist, those that are suitable for our growth and sustenance and those that cause us blood and bad health.

What is Theory of Relativity?

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I have read so many complicated description of whats theory of relativity that I tend to think such complicacy serves two purposes;

Misleading: it takes us away from the real concepts.

Complicated: It does not make the concepts easy at all to grasp.

Ineffective: It ill-prepares even very good students — as their precious time is wasted and the mediocre rejoice.

Here is an appropriate description of relativity theory.

Relative as suggests hinges on in reference to what? So you may call it a reference-dependent theory. But if you understand what theory of relativity is you may as well call it an equivalence theory.

This theory establishes for the first time in greater depth the equivalence of many ideas, concepts, physical laws and methods. This is the work of Albert Einstein. But if you dig deeper you will see that most of the concepts were known before, and classical physics is capable of producing these ideas 1st hand.

It is for no strange reason relativity theory is included as classical physics, in greater conceptual frameworks. Its because its merely a more refined calculation of certain problems, some of which were known and some which were not, but never to the extent and power of the methods of Einstein.

Einstein eg solved the problem of perihelion of mercury very exactly which was not as exactly understood in the canonical formulations of the old classical theory, so theory of relativity is the new classical theory.

But there are two episodes of this story.

1. Special theory of relativity: this is a regime of the theory of relativity where it pertains exclusively to kinetic energy: