Tuesday, October 26, 2010

Physics 3 - Acceleration & free fall

Physics 4 - Angular Velocity

Angular Acceleration

Physics 5 - Angular acceleration & linear-angular analogy

Velocity and Acceleration

One of a series of 7 physics videos made for 1st year 'A' level students by Hertfordshire teachers in June/July 1984.
Use the search tag 'HSCphysics' to find the other 6 videos.

Fun with Physics - Angular Momentum

physics students get an up close and personal experience with angular momentum on a playground

Module 2 - Lecture 2 - Inertia Tensor & Angular Momentum

Lecture Series on Dynamics of Machines by Prof. Amitabha Ghosh
Department of Mechanical Engineering IIT Kanpur

Introduction to angular velocity

Angular velocity or how fast something is spinning.

Physics 4 - Angular Velocity

Physics: Rotational kinematics and torque (2)

Physics: Rotational kinematics. Angular displacement (Δθ); angular velocity (ω); angular acceleration (α). Torque

Physics: Rotational kinematics and torque (1)

Physics: Rotational kinematics. Angular displacement (Δθ); angular velocity (ω); angular acceleration (α). Torque

Physics: Work. Conservation of energy (3)

Physics: Kinetic energy. Work. Gravitational potential energy. Total mechanical energy. Conservation of mechanical energy. Spring potential energy. Conservation of energy problems

Physics: Work. Conservation of energy (2)

Physics: Kinetic energy. Work. Gravitational potential energy. Total mechanical energy. Conservation of mechanical energy. Spring potential energy. Conservation of energy problem

Physics: Work. Conservation of energy (1)

Physics: Kinetic energy. Work. Gravitational potential energy. Total mechanical energy. Conservation of mechanical energy. Spring potential energy. Conservation of energy problems

Physics: Two-dimensional kinematics (2)

Physics: How to solve kinematics problems about general two-dimensional motion.

Physics: Two-dimensional kinematics (1)

Physics: How to solve kinematics problems about general two-dimensional motion.

Multi-part one-dimensional motion problems (2)

Physics: Multi-part one-dimensional kinematics problems. A multiple-object kinematics problem

This is a recording of a tutoring session, posted with the students' permission

Multi-part one-dimensional motion problems (1)

Physics: Multi-part one-dimensional kinematics problems. A multiple-object kinematics problem

This is a recording of a tutoring session, posted with the students' permission.

More on one-dimensional kinematics (3)

One-dimensional kinematics. Unit conversion; metric prefixes. Time, position, displacement, velocity, acceleration. Vectors vs. scalars; vector arrows. Using the kinematics equations—a problem. How to do problems with zero acceleration (i.e., constant velocity). A two-object kinematics problem

More on one-dimensional kinematics (2)

One-dimensional kinematics. Unit conversion; metric prefixes. Time, position, displacement, velocity, acceleration. Vectors vs. scalars; vector arrows. Using the kinematics equations—a problem. How to do problems with zero acceleration (i.e., constant velocity). A two-object kinematics problem

Physics: How to solve kinematics problems about general one-dimensional motion with constant acceleration.

Physics: Using Newton's second law (5)

Physics: Force. Newton's first law of motion; Newton's second law of motion; Newton's third law of motion. Using Newton's second law to solve dynamics problems. Weight. Ropes and tension. Normal force. Inclined planes. Kinetic friction; static friction

Physics: Using Newton's second law (4)

Physics: Force. Newton's first law of motion; Newton's second law of motion; Newton's third law of motion. Using Newton's second law to solve dynamics problems. Weight. Ropes and tension. Normal force. Inclined planes. Kinetic friction; static friction

Physics: Using Newton's second law (3)

Physics: Force. Newton's first law of motion; Newton's second law of motion; Newton's third law of motion. Using Newton's second law to solve dynamics problems. Weight. Ropes and tension. Normal force. Inclined planes. Kinetic friction; static friction

Physics: Using Newton's second law (2)

Physics: Force. Newton's first law of motion; Newton's second law of motion; Newton's third law of motion. Using Newton's second law to solve dynamics problems. Weight. Ropes and tension. Normal force. Inclined planes. Kinetic friction; static friction

Physics: Using Newton's second law (1)

Physics: Force. Newton's first law of motion; Newton's second law of motion; Newton's third law of motion. Using Newton's second law to solve dynamics problems. Weight. Ropes and tension. Normal force. Inclined planes. Kinetic friction; static friction
Physics: Force. Newton's first law of motion; Newton's second law of motion; Newton's third law of motion. Using Newton's second law to solve dynamics problems. Weight. Ropes and tension. Normal force. Inclined planes. Kinetic friction; static friction

Physics & Electromagnetism : What Affects the Strength of an Electromagnet?

The strength of an electromagnet is directly related to the number of turns in the wire coil that is used to make the magnet. Discover how to increase the current to increase the strength of electromagnets with help from a science teacher in this free video on electromagnets and physics

Physics & Electromagnetism : How to Make an Electromagnet

An electromagnet, as opposed to a permanent magnet, can be switched off and designed to provide greater strength. Find out how to wrap a coil wire to make an electromagnet with help from a science teacher in this free video on electromagnets and physics.

Physics & Electromagnetism : How to Turn on a Light Bulb With a Battery

ENERGY FROM THE SUN

IT IS OBVIOUS THAT ENERGY CCCCCCAN BE CREATED FROM THE SUN BUT THIS VIDES CONFIRMS THIS FACT BY EVEVRY POINT OF VIEW

Physics: Using Newton's second law (1)

NEWTON THREE LAWS OF MOTION VIDEO DESCRIPTION

AMAZING PHYSICS

THERE IS AMAZING USE OF ELECTROMAGNETSISM HERE

physics genral

Atmospheric Chemistry and Physics (ACP) is an international scientific journal dedicated to the publication and public discussion of high quality studies investigating the Earth's atmosphere and the underlying chemical and physical processes. It covers the altitude range from the land and ocean surface up to the turbopause, including the troposphere, stratosphere and mesosphere.

The main subject areas comprise atmospheric modelling, field measurements, remote sensing, and laboratory studies of gases, aerosols, clouds and precipitation, isotopes, radiation, dynamics, biosphere interactions, and hydrosphere interactions (for details see Journal Subject Areas). The journal scope is focused on studies with general implications for atmospheric science rather than investigations that are primarily of local or technical interest. The manuscript types considered for peer-reviewed publication are research articles, review articles, technical notes and commentaries/replies.

Atmospheric Chemistry and Physics has an innovative two-stage publication process involving the scientific discussion forum Atmospheric Chemistry and Physics Discussions (ACPD), which has been designed to:

foster and provide a lasting record of scientific discussion;
maximise the effectiveness and transparency of scientific quality assurance;
enable rapid publication of new scientific results;
make scientific publications freely accessible.
In the first stage, papers that pass a rapid access peer-review are immediately published on the Atmospheric Chemistry and Physics Discussions (ACPD) website. They are then subject to Interactive Public Discussion, during which the referees' comments (anonymous or attributed), additional short comments by other members of the scientific community (attributed) and the authors' replies are also published in ACPD. In the second stage, the peer-review process is completed and, if accepted, the final revised papers are published in ACP. To ensure publication precedence for authors, and to provide a lasting record of scientific discussion, ACPD and ACP are both ISSN-registered, permanently archived and fully citable.

Atmospheric Chemistry and Physics also offers an efficient new way of publishing special issues, in which the individual papers are published as soon as available and linked electronically (for more information see Special Issues).

PHYSICS TECHNOLOGIES


this means that the driver of the computer market will pretty much be nothing more than replacement due to losses of breaking.


Of course, there are other uses of these technologies in the form of newer iPads and other handheld computers that will become more powerful and more flexible, but even those will hit their limit sometime around 2020 or so, with perhaps a few years extra before someone obtains an optimized design with all the best possible features.


Chip manufacturers will undergo radical downsizing, unless they can get into the markets for medical nano technology or nano manufacturing of other production related devices.

Imagine if Intel, Apple, AMD, Nintendo, Microsoft*, Cysco, and IBM all had to downsize by 10% to 50% within a matter of a few years. Well, microsoft has some padding because they are obviously far more about software than hardware, but even they would need to downsize if there isn't an all new generation of computer being cranked out every year.


There are only so many things that you can put a computer chip in, and it would start to get ridiculously redundant to be putting a super computer in everything anyone makes.

I'm talking about more than just a tech bubble, but a permanent tech plateau which rarely, if ever, goes up again afterwards...480" height="385">

Computer Reads And Understands Text, A.I. component

One of the things I have spent some time thinking about is the way computers communicate with humans. Throughout the history of modern computers, it has been a dream for being able to program a computer in a natural human language.

In the past, I have known of some systems that use xml to simulate a computer that understands grammar and syntax of the english language, and is therefore able to read, understand, and even reply to basic questions, when it knows the answer.

There have also been competitions such as programing a computer in this way, then people try to guess whether they are paired witha human on the other side, or whether it's a fully automated system they are communicating with.


In considering how to do this, I thought of making a "compiler" that treats the english language as a programming language of sorts.

We begin by parsing a sentence, breaking it down to individual words. There will actually be a class definition called "word", and it's data member is a string equal to that word, along with functions and operators that will help determine how words interact with one another.

In order to make a learning engine, we might need a system that has the best of both dynamic aspects as well as hard coded aspects, thus the system begins with most common words already having their definitions. For example, we would have a list of prepositions and code modeling how they modify their objects, another list for adverbs, adjectives, conjunctions, and pronouns, etc.

Together, the functionality of these "word" objects would convey the meaning of a sentence in a form which the computer can "understand," both individually and in it's context within a paragraph, and then the meaning of the paragraph within a chapter, section, or sub-section of a book.


The ultimate goal would be:

1) The ability of the software to identify the most important and relevant information from an article, and sumarize the article in it's own words, without further human input.

2) The ability of the software to read, understand, and combine factual inputs from multiple articles or books by one or more authors, and generate accurate, factual reports, both in it's own words and using quoted references when needed.



This implies "teaching" the machine to a relevant skill level with respect to the content of the articles, and with respect to the language involved.


For example, if it is reading a math or science article, and the derivative is mentioned, it needs to know from context that it is talking about the mathematical construct used to calculate the rate of change, along with it's various other applications and definitions. But it also needs to know that, under the context, the paragraph is mentioning the derivative, and not telling the computer to solve for a derivative. On the other hand, if the paragraph actually is telling the reader to solve for a particular derivative, the computer needs to be able to figure that out too.


The text is the name of the word, and the code would simulate the applications, function, and meaning of the word given it's context.


I intend to do this with PHP due to the flexibility and power of PHP's parsing and data architectures.


Obviously, I am dealing with not only storing text, but obtaining, storing, and understanding, and then applying all knowledge to a generalized problem or a specific problem, such as helping humans find relevant articles, books, or journals on the internet, and quickly summarizing or even explaining them to the reader. It would be sort of like Google, except that it isn't merely indexing or finding connections or common phrases, but actually understanding and applying the knowledge of the articles, books, or journals it reads.

In theory, you could start it off the same way humans are trained from toddler upward, with story books, readers, history, and science texts of each successive grade level. A huge advantage to the machine would be permanent file access to multiple texts, dictionary, and encyclopedia on all topics.


This is an extremely large undertaking, bordering on true A.I. in many respects, but I believe it is something that is doable, as it is a matter of pure logic and data storage.

Is Tv A Type Of Generalized Hallucination?, The reality and physics of TV

This discussion raises very serious, original, and important (and downright disturbing) questions about the effects, and safety, of the technological invention called television viewing. What exactly are the physics of television?

===========================
The overeating during television occurs in keeping with the fact that TV is an extended, interactive, and unnatural form of dream vision AS waking vision. Bodily feeling/sensation is therefore reduced during TV (as is the case during dream experience), so the feeling of fullness is reduced/lacking. Dr. Joyce Starr agrees with this as well. (Television is an unnatural creation of generalized thought; accordingly, TV may be held to be a generalized hallucination.) The experience of sound and vision in/as TV is even more like thought than in the case of the vision and sound in the dream.

Emotion is manifest as sensory experience and feeling.

TV involves emotional detachment, disintegration, contraction, and loss; and this certainly relates to (or involves) depression and anxiety as well. Importantly, TV also reduces memory and thought; and this is also consistent with/similar to dream experience. Hence, the overeating while watching television relates to the reduction in thought and memory as well.

Television is only possible because this disintegration, reconfiguration, contraction (i.e., compression), and extension of visual sensory experience occurs during dreams. Accordingly, both television viewing and dreams may be said to include (or involve) reduced ability to think, anxiety, and increased distractibility. Television thus compels attention, as it is compelled in the dream; but it is an unnatural and hallucinatory experience. Hence, television is addictive. Similar to the visual experience while dreaming, television compels attention to the relative exclusion of other experience. Television reduces consciousness and results in a flattening of the visual experience as a result of combining waking visual experience with relatively unconscious visual experience. Television involves the experience of what is less animate, for it involves a significant reduction in (or loss of) visual experience. This disintegration of the visual experience (as in the dream) also results in an emotional disintegration (i.e., anxiety). That television may be so described (and even possible) is hard to imagine; but this is consistent with the fact that it took so very many different minds (and thoughts) of genius in order to make the relatively unconscious visual experience of the dream conscious. Since the thinking that is involved in making the experience of television possible is so enormously difficult, it becomes difficult to think while partaking of that experience. Television may be seen as an accelerated form or experience of art, thereby making someone less wary (or less anxious) initially, but less creative and more anxious (as time passes) as the advance of the self becomes unsustainable. The experience (or effects) of television demonstrates the interactive nature of being and experience; for, in the dream, there is also a reduction in the totality (or extensiveness) of experience.

Thought involves a relative reduction in the range and extensiveness of feeling. In keeping with this, dreams make thought more like sensory experience in general. Accordingly, both thought and also the range and extensiveness of feeling are proportionately reduced in the dream. (This reduction in the range and extensiveness of feeling during dreams is consistent with the fact that the experience of smell very rarely occurs therein.) Since there is a proportionate reduction of both thought and feeling during dreams, the experience of the body is generally (or significantly) lacking; for thought is fundamentally rendered more like sensory experience in general. Thoughts and emotions are differentiated feelings. By involving the mid-range of feeling between thought and sense, dreams make thought more like sensory experience in general. The reduction in the range and extensiveness of feeling during dreams is why there is less memory and thought therein.

Dream vision is generally closer (or flattened), thereby resulting in a loss/reduction of peripheral vision as well. Comparatively, television further flattens vision; and it also involves a reduction in peripheral vision.

In the dream, vision and thought are semi-detached from touch (and feeling). One may or may not be able to touch what is seen in the dream. In the visual experience that is television, the visual images may not be (and are not) touched at all. In the case of waking vision, one can [generally] touch what one sees.

It is not only in the dream that the vision of each individual person is necessarily different. That is obvious. Importantly, the experience of television is uniquely that of the individual.

Television may be understood as a creation of generalized thought. The ability of thought to describe or reconfigure sense is ultimately dependent upon the extent to which thought is similar to sense.

Television makes thought even more like vision than in the dream, thereby reducing thought and vision. Thoughts are relatively shifting and variable. Likewise, dream vision is relatively shifting and variable. In the case (and form) of television, the visual images become more shifting and variable than that of the dream; and this is in keeping with attention being compelled and sustained in conjunction with these images being even more like (or consistent with) thought. People tend to believe what they see (and hear) during television.

Ordinary (and natural) vision is removed and replaced in the case of television. Unlike art, which can be the interactive creation of any one person, television is impossible for any one person to possibly create or otherwise experience.

Television is an hallucination. Hallucinations are already known to be connected with/associated with/”caused by” all sorts of very serious mental/physical/emotional conditions or disorders. It is undeniable that this is a very important and serious matter.
=======================
The fundamentally interactive and significant/pervasive effects of TV/modern physics are called into question here. Autism is known to involve sensory processing disorders, for example.

Can we just reconfigure, replace, and alter the manifestations of sensory experience (including the range and extensiveness of feeling thereof) at will -- without consequences to our health, bodies, emotions, thought, feelings, language, and perceptions?

This is a very important discussion about the consequences of "outsmarting experience/vision" via/with technology.

Questions and comments welcome please. Thanks.

Quantum Error Correction

Publication in Nature Photonics: European researchers report a quantum error correcting code

The magazine Nature Photonics publishes in this week issue an article about the successful demonstration of a quantum error correcting code by the laboratory of Ulrik Andersen at the Technical University of Copenhagen, Denmark. This work, resulting from an international collaboration with the teams of Gerd Leuchs at the Max Planck Institute for the Science of Light in Erlangen, Germany, and of Nicolas Cerf at Université Libre de Bruxelles, Belgium, offers the prospects to enable tomorrow's information technologies based on quanta.

The computers of the future, currently developed in many laboratories worldwide, will use increasingly miniaturized components. The ultimate stage of this development is expected to reply on the manipulation of quantum bits, analogous to bits - the computer's 0 and 1's - but at the level of atoms and photons, which are the elementary constituents of matter and light. Quantum physics prevails at the microscopic scale, so that quantum computers, which would exploit information quanta at this scale, are some of the most awaited applications of this new information technology.

The article by Mikael Lassen and collaborators, which appears in Nature Photonics, reports on an important future component for quantum information technology, namely a quantum error correcting code.

We actually use error correcting codes every day without knowing it ! CDs and DVDs use this technique to enable a reading that is relatively insensitive to small imperfections on the disk surface such as scratches, smudges or dust.

The Danish team and its Belgian and German colleagues have implemented an error correcting code that provides resistance to errors in the handling, transmission or storage of quanta of information. Their scheme, using the transmission of photons, resists the loss thereof. Quantum information is split into several light beams and can be recovered even if photons of these beams have been lost.

Such an insensitivity is remarkable as information quanta are deemed extremely fragile: the loss of one or a few photons, almost imperceptible particles of light constituting a beam, is an often inevitable process.

This experiment is one of the first demonstration of error correction achieved at the scale of quanta and should help paving the way to computers of the future.



* Full bibliographic informationQuantum optical coherence can survive photon losses using a continuous-variable quantum erasure-correcting code
Mikael Lassen, Metin Sabuncu, Alexander Huck, Julien Niset, Gerd Leuchs, Nicolas J. Cerf & Ulrik L. Andersen
Nature Photonics October 2010, pp700 - 705

Prediction / Onesimpleprinciple, Prediction / onesimpleprinciple

During the solar eclipse, the pendulum will go mess

Check out my latest text here.

http://www.onesimpleprinciple.com/forum/viewforum.php?f=2

Updated front page even better text which is not yet in English.

Google translator to translate, but not very well.

www.onesimpleprinciple.com

Later also front page with english

The Mechanics Of Time

I have derived a unifying paper that describes everything under the referenced observation of time. I described it mathematically however the math requires a firm grasp of reference frames. Needless to say, you can understand calculus but can have little clue about physics at the same time. So I have been rewriting my work in order to simplify the excessive use of reference. I am at wits end.

I don't know how to explain this line any clearer, "Any measurable system is the ratio of its attractive and repelling fields."[I]

That means that gravity will attract you to a planet but the electric field will stop you. That means an electron will be pulled by the nucleus but will stop short. That means a substance can be a liquid, have heat but still be bound. Or a substance can be a gas, have heat and not be bound.

If that rule didn't exist, things would collapse into singularities or evaporate into nothing. With out this ratio, nothing would have dimension to exist. It would be impossible to measure something that didn't follow this rule. It applies in every field of science. I CAN PROVE IT MATHEMATICALLY.

I seem to be able to keep the legitimacy of this statement until I use it as an actual law. That is to say the universe itself as a system would have to play by the same rule. That the universe is the ratio of gravitational and dark energy dilation.

Before I type out any more ranting I'll just ask that anyone who reads this legitimately attempt to prove or disprove. Don't just scoff it off because you didn't pay attention in physics class.

Burkhard Heim's Particle Structure Theory



This thread is for the purpose of discussing a Theory by Burkhard Heim, published in the Journal of Scientific Exploration in 1992. [vol. 6, no.3, pp. 217-231]
Authors: T. Auerbach, I. von Ludwiger

Also related would be the nature of mass, gravity, and the nature of dimensions.


To start, here is the link to the paper.

The introduction:

The present article provides an overview of Burkhard Heim´s unified field theory of elementary particles and their internal structures (heim,1984,1989; v.Ludwiger, 1981). Various old and new concepts enter into the theory, including cosmology, quantum field theory, organizing processes similar to Sheldrake’s morphogenetic fields (Sheldrake, 1985), and the existence of a smallest area in a 6-dimensional world. The main results of Heim’s theory are formulas for the masses of elementary particles. Results turn out to be in very good agreement with measured values.

This report is written with the aim of describing the basic architecture of Heim´s theory in mainly non-technical terms for the benefit of the average JSE reader with a scientific background, who is not necessarily a physicist. For this reason the terminology of field theory is often replaced by less specific but more readily comprehensible expressions. In an Appendix selected topics are discussed in more technical terms for the benefit of physicists.

The abstact:

Heim´s Theory is defined in a 6-dimensional world, in 2 dimensions of which events take place that organize processes in the 3 dimensions of our experience. A very small natural constant, called a “metron“, is derived, representing the smallest area that can exist in nature. This lead to the conclusion that space must be composed of a 6-dimensional geometric lattice of very small cells bounded on all sides by metrons. The existence of metrons requires our usual infinitesimal calculus to be replaced by one of finite areas. The unperturbed lattice represents empty vacuum. Local deformations of the lattice indicate of something other than empty space. If the deformation is of the right form and complexity it acquires the property of mass and inertia. Elementary particles are complex dynamical systems of locally confined interacting lattice distortions. Thus the theory geometricizes the world by viewing it as a huge assemblage of very small deformations of a 6-dimensional lattice in vacuum. The theory also has significant consequences for cosmology. width="640" height="385">

Gravity,electromagnetism,inertia,quantum Gravity, ... the requirements of unification

Since the self ultimately represents, forms, and experiences a comprehensive approximation of the totality of experience by combining conscious and unconscious experience, then our growth and our being/becoming other than we are necessarily requires and involves a fundamental extension, integration, and transcendency of the laws/forces of physics.

The extension of the self in and with time and space is demonstrative of (and requires) the union of gravity and electromagnetism. Indeed, the experience of the body is inseparable from the laws/forces of physics.

It is impossible that the mathematical union of Einstein's theory of gravity and Maxwell's theory of light/electromagnetism is a meaningless coincidence or an error.

This union must be plainly and signficantly present/manifest in our experience.

The structure and form of thought is generally reflected in the structure of experience, and this is ultimately reflected in the laws/forces of physics.

This also reveals the limits of physics, as the ability of thought to describe (including mathematically) OR reconfigure (as in dreams) sense is ultimately dependent upon the extent to which thought is similar to sensory experience. Indeed, this accounts for the "unreasonable effectiveness" of mathematics.

Thought is fundamentally quantum mechanical, gravitational, electromagnetic, and inertial in its constitution, structure, and form.

The [Einstein/Maxwell] mathematical unification in a fourth spatial dimension indicates space that is stretched and thereby flattened, as the result of combining a larger and smaller space. In unifying gravity and electromagnetism, balanced attraction and repulsion average/reduce gravity in conjunction with relatively increased inertia and relatively decreased gravity, on balance.

Can F=ma demonstrate quantum gravity? Yes, when distance in space is averaged/reduced in conjunction with fundamentally balanced repulsion and attraction and increased inertia that is offset by/balanced with reduced gravity. Space then manifests as gravitational/electromagnetic energy, as gravitational contraction may be understood as being balanced by/offset with electromagnetic repulsion. Such a stable, fundamental, and balanced [distance in] space requires that an inherently larger space and an inherently smaller space be combined.

These are the theoretical requirements of quantum gravity and of space manifesting as inertial/gravitational/electromagnetic binding energy.

When space is smaller and larger, inertia is relatively increased, and gravity is proportionately reduced accordingly.

Balanced and fundamental inetia and gravity/accel. are equivalent manifestations of the same thing. This fixes/determines BOTH distance in space AND position relative to distance in space. This requires balanced attraction and repulsion as binding energy.

Gravity is key to distance in space. You will never understand the union of inertia, gravity/accel., and electromagnetism until you understand this. You must balance/equate gravity, inertia, and electromagnetism/light in conjunction with balanced and fundamental scale/distance and attraction/repulsion. Dreams accomplish all of this.

The middle distance of gravity allows for an averaging/reduction of gravity while also allowing for an increase (on balance) of inertia. This is how to fundamentally balance and unite scale/distance in space, attraction/repulsion, and inertia/gravity/electromagnetism. Growth and the union of it all from the center. Thought and feeling are BOTH proportionately reduced in dreams TO/AT the center of the body. Thoughts and emotions are differentiated FEELINGS.

Dreams involve a fundamental integration AND spreading of being, experience, and thought at the [gravitational] mid-range of feeling between thought and sensory experience.

The baby grows at/near the center of the body.

Question and comments welcome. Keep an open mind. Thanks.

MOMENTUM CONCEPTS

Momentum is mass times velocity. It is a vector.



Angular momentum is the cross-product of position and momentum. Being the cross-product of two vectors, it is technically a pseudovector, although it is normally referred to simply as a vector.



For a rigid body, angular momentum is also the ordinary product of moment of inertia (a scalar) and angular velocity (a pseudovector).



Momentum appears directly in Newton's second law, and angular momentum appears on taking the cross-product of Newton's second law with displacement.

Equations
By Newton's second law, Net Force = Rate of change of Momentum:



By taking the cross-product of the above with the position vector from any fixed point, we find that net Torque about that point = Rate of change of Angular Momentum about that point:
1. Informal introduction to momentum

Supposing a mosquito approaches you with the velocity of 40 km/h. Even a collision would hardly affect you. However, if a truck was to approach you with the same velocity, it could be fatal. It naturally, is because of the truck's mass. However, it is not only mass that plays a role here. If it were, a truck standing still would've scared you too. Hence, an important property here is the product of mass and velocity. This product is known as momentum.

Momentum is a very important property of closed systems, as it allows us to predict the behavior of such systems.

2. Law of conservation of momentum

A closed system, is a system in which no external force applies. In such a system, the linear momentum does not change. This can be followed from the alternative definition of force i.e. rate of change of momentum. When force is zero, there is no change in momentum.

Internal forces may act, as in a collision, but they cancel out each other. This follows from Newton's Third Law of motion. Not only a collision, but even in the case where two charged particles attract each other and brought towards/away from each other, the motion is such that the linear momentum is always the same. If the system was initially at rest, the linear momentum will continue to be zero.

In the case of angular momentum, when no external Torque is applied on a system, there is no change in angular momentum.

2A. Vector components

Momentum is a vector, and so any equation involving momentum applies to the components in each direction separately.

In particular, even in a system with external forces, conservation of components of momentum will still apply in any direction in which there is no external force: for example, it will apply to the horizontal components of momentum of balls on a horizontal pool table, even if the pool table is accelerating vertically (because all the external forces are vertical).

3. Applications of conservation of momentum

Supposing, a sphere is moving with the velocity in the east direction. It explodes into two parts of equal masses, A and B. If it is found that A moves in the southwest direction with speed , we can use the conservation of momentum to find out the velocity of B.

Let the mass of the sphere be M. Then, the initial momentum of the sphere was:



Now, the momentum of A can be given as:



i.e.:



Since they break in two parts, and A lies in the XY plane, B has to be in the XY plane as well. If it were not, then there would be an additional component along the which would not be canceled, and hence the conservation law cannot be satisfied.

Let, the momentum of B be . The momentum of a system is the same of the momentum of it's particles. Hence, the momentum of this system at this instant is given as:





This must equal the initial momentum, since no external force acted on the system. Hence, on equation the two momenta, we get:



Hence, we were able to arrive at the velocity vector for the particle B. In collision systems, the Kinetic Energy may or may not conserved, since it is converted to other forms of energy like heat, sound and light. However, both linear and angular momentum is always conserved when no external force and torque act on the system.

4. Momentum and system of particles

If there are a number of particles and their linear momentum is needed, then the linear momentum is defined as the product of the mass of the system and the velocity of the center of mass of the system.

In previous examples of collisions and explosions, when we say that the momentum of a system is conserved, it implies that the velocity of the center of mass of the system does not change.

5. Impulse

Another important quantity is Impulse. Impulse has the same units as that of Momentum. Impulse is defined as a change in momentum, which is brought on by an acting force. Impulse is commonly denoted by 'j'. It is a vector quantity, since it is the difference of two vector quantities. Momentum can be defined as the time integral of Force. When on a system having momentum , a force F acts, for a time 't' from to , and changes the system of the momentum to , then the change in momentum of the system is defined as the 'Impulse' that acted on the system. This is written as:



This definition is sometimes helpful in calculating the force in same cases.

For example, consider the attached image: if a ball hits a wall at and rebounds at on the other side of the axis with the same speed , then the impulse is defined as:



If we assume that in a small time 't', a constant force F acted on the ball, by the definition above, we can say that:



or:



6. Momentum in modern physics

A change in momentum of a particle, under classical physics is brought about only by a change in it's velocity. However, under Relativity, a change in momentum also occurs due to a change in mass due to Mass dilation. Hence, momentum is now defined as:



where, is the Lorentz factor and is the rest mass of the particle. This article however, is focused on the classical physics definition of momentum, and hence we shall not discuss it in further detail.

Even massless particles, like the photon have momentum. The significance of momentum in this case again is that the momentum is conserved when a photon collides with another particle or is absorbed by it. The momentum for such particles is defined as: