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Physics (from Ancient Greek: φύσις physis "nature") is a natural science that involves the studyof matter[1] and its motion through space and time, along with related concepts such as energyand force.[2] More broadly, it is the general analysis of nature, conducted in order to understandhow the universe behaves.[3][4][5]Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizesknowledge in the form of testable explanations and predictions about the universe.[1] In an older andclosely related meaning (found, for example, in Aristotle), "science" refers to the body of reliableknowledge itself, of the type that can be logically and rationally explained (see History and philosophybelow).[2] Since classical antiquity science as a type of knowledge was closely linked to philosophy. In theearly modern era the words "science" and "philosophy" were sometimes used interchangeably in theEnglish language. By the 17th century, natural philosophy (which is today called "natural science") wasconsidered a separate branch of philosophy.[3] However, "science" continued to be used in a broadsense denoting reliable knowledge about a topic, in the same way it is still used in modern terms such aslibrary science or political science. The branches of science (which are also referred to as "sciences", "scientific fields", or "scientificdisciplines") are commonly divided into two major groups: natural sciences, which study naturalphenomena (including biological life), and social sciences, which study human behavior and societies.These groupings are empirical sciences, which means the knowledge must be based on observablephenomena and capable of being tested for its validity by other researchers working under the sameconditions.[1] There are also related disciplines that are grouped into interdisciplinary and appliedsciences, such as engineering and medicine. Within these categories are specialized scientific fields thatcan include parts of other scientific disciplines but often possess their own terminology and expertise.[2]PHYSICSPhysics is the science of matter and energy, and the movement and interactions between themboth.The most popular branches of physics are: mechanics electromagnetism heat and thermodynamics atomic theory relativity astrophysics theoretical physics optics, geophysics biophysics particle physics sound light atomic and molecular physics
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nuclear physics solid state physics plasma physics geophysics biophysicsThe two main branches are : 1) Classical Mechanics 2) Quantum MechanicsThis article is about thephysics sub-field. For the book written by Herbert Goldstein and others, see Classical Mechanics(book). Classical mechanics History of classical mechanics Timeline of classical mechanics Branches[show] Formulations[show] Fundamental concepts[show] Core topics[show] Scientists[show] v t eIn physics, classical mechanics is one of the two major sub-fields of mechanics, which isconcerned with the set of physical laws describing the motion of bodies under the action of asystem of forces. The study of the motion of bodies is an ancient one, making classicalmechanics one of the oldest and largest subjects in science, engineering and technology.Classical mechanics describes the motion of macroscopic objects, from projectiles to parts ofmachinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies.Besides this, many specializations within the subject deal with gases, liquids, solids, and otherspecific sub-topics. Classical mechanics provides extremely accurate results as long as thedomain of study is restricted to large objects and the speeds involved do not approach the speedof light. When the objects being dealt with become sufficiently small, it becomes necessary to
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introduce the other major sub-field of mechanics, quantum mechanics, which reconciles themacroscopic laws of physics with the atomic nature of matter and handles the wave–particleduality of atoms and molecules. In the case of high velocity objects approaching the speed oflight, classical mechanics is enhanced by special relativity. General relativity unifies specialrelativity with Newtons law of universal gravitation, allowing physicists to handle gravitation ata deeper level.The term classical mechanics was coined in the early 20th century to describe the system ofphysics begun by Isaac Newton and many contemporary 17th century natural philosophers,building upon the earlier astronomical theories of Johannes Kepler, which in turn were based onthe precise observations of Tycho Brahe and the studies of terrestrial projectile motion ofGalileo. Since these aspects of physics were developed long before the emergence of quantumphysics and relativity, some sources exclude Einsteins theory of relativity from this category.However, a number of modern sources do include relativistic mechanics, which in their viewrepresents classical mechanics in its most developed and most accurate form.[note 1]The initial stage in the development of classical mechanics is often referred to as Newtonianmechanics, and is associated with the physical concepts employed by and the mathematicalmethods invented by Newton himself, in parallel with Leibniz, and others. This is furtherdescribed in the following sections. Later, more abstract and general methods were developed,leading to reformulations of classical mechanics known as Lagrangian mechanics andHamiltonian mechanics. These advances were largely made in the 18th and 19th centuries, andthey extend substantially beyond Newtons work, particularly through their use of analyticalmechanics. Ultimately, the mathematics developed for these were central to the creation ofquantum mechanics.Contents 1 History 2 Description of the theory o 2.1 Position and its derivatives 2.1.1 Velocity and speed 2.1.2 Acceleration 2.1.3 Frames of reference o 2.2 Forces; Newtons second law o 2.3 Work and energy o 2.4 Beyond Newtons laws 3 Limits of validity o 3.1 The Newtonian approximation to special relativity o 3.2 The classical approximation to quantum mechanics 4 Branches 5 See also 6 Notes 7 References 8 Further reading
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9 External linksHistoryMain article: History of classical mechanicsSee also: Timeline of classical mechanics Classical Physics Wave equation History of physics Founders[show] Branches[show] Scientists[show] v t eSome Greek philosophers of antiquity, among them Aristotle, founder of Aristotelian physics,may have been the first to maintain the idea that "everything happens for a reason" and thattheoretical principles can assist in the understanding of nature. While to a modern reader, manyof these preserved ideas come forth as eminently reasonable, there is a conspicuous lack of bothmathematical theory and controlled experiment, as we know it. These both turned out to bedecisive factors in forming modern science, and they started out with classical mechanics.The medieval "science of weights" (i.e., mechanics) owes much of its importance to the work ofJordanus de Nemore. In the Elementa super demonstrationem ponderum, he introduces theconcept of "positional gravity" and the use of component forces.
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Three stage Theory of impetus according to Albert of Saxony.The first published causal explanation of the motions of planets was Johannes KeplersAstronomia nova published in 1609. He concluded, based on Tycho Brahes observations of theorbit of Mars, that the orbits were ellipses. This break with ancient thought was happeningaround the same time that Galileo was proposing abstract mathematical laws for the motion ofobjects. He may (or may not) have performed the famous experiment of dropping two cannonballs of different weights from the tower of Pisa, showing that they both hit the ground at thesame time. The reality of this experiment is disputed, but, more importantly, he did carry outquantitative experiments by rolling balls on an inclined plane. His theory of accelerated motionderived from the results of such experiments, and forms a cornerstone of classical mechanics.Sir Isaac Newton (1643–1727), an influential figure in the history of physics and whose threelaws of motion form the basis of classical mechanicsAs foundation for his principles of natural philosophy, Isaac Newton proposed three laws ofmotion: the law of inertia, his second law of acceleration (mentioned above), and the law of
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action and reaction; and hence laid the foundations for classical mechanics. Both Newtonssecond and third laws were given proper scientific and mathematical treatment in NewtonsPhilosophiæ Naturalis Principia Mathematica, which distinguishes them from earlier attempts atexplaining similar phenomena, which were either incomplete, incorrect, or given little accuratemathematical expression. Newton also enunciated the principles of conservation of momentumand angular momentum. In mechanics, Newton was also the first to provide the first correctscientific and mathematical formulation of gravity in Newtons law of universal gravitation. Thecombination of Newtons laws of motion and gravitation provide the fullest and most accuratedescription of classical mechanics. He demonstrated that these laws apply to everyday objects aswell as to celestial objects. In particular, he obtained a theoretical explanation of Keplers laws ofmotion of the planets.Newton previously invented the calculus, of mathematics, and used it to perform themathematical calculations. For acceptability, his book, the Principia, was formulated entirely interms of the long-established geometric methods, which were soon to be eclipsed by his calculus.However it was Leibniz who developed the notation of the derivative and integral preferred[citationneeded] today.Hamiltons greatest contribution is perhaps the reformulation of Newtonian mechanics, nowcalled Hamiltonian mechanics.Newton, and most of his contemporaries, with the notable exception of Huygens, worked on theassumption that classical mechanics would be able to explain all phenomena, including light, inthe form of geometric optics. Even when discovering the so-called Newtons rings (a waveinterference phenomenon) his explanation remained with his own corpuscular theory of light.After Newton, classical mechanics became a principal field of study in mathematics as well asphysics. After Newton there were several re-formulations which progressively allowed a solutionto be found to a far greater number of problems. The first notable re-formulation was in 1788 byJoseph Louis Lagrange. Lagrangian mechanics was in turn re-formulated in 1833 by WilliamRowan Hamilton.
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Some difficulties were discovered in the late 19th century that could only be resolved by moremodern physics. Some of these difficulties related to compatibility with electromagnetic theory,and the famous Michelson–Morley experiment. The resolution of these problems led to thespecial theory of relativity, often included in the term classical mechanics.A second set of difficulties were related to thermodynamics. When combined withthermodynamics, classical mechanics leads to the Gibbs paradox of classical statisticalmechanics, in which entropy is not a well-defined quantity. Black-body radiation was notexplained without the introduction of quanta. As experiments reached the atomic level, classicalmechanics failed to explain, even approximately, such basic things as the energy levels and sizesof atoms and the photo-electric effect. The effort at resolving these problems led to thedevelopment of quantum mechanics.Since the end of the 20th century, the place of classical mechanics in physics has been no longerthat of an independent theory. Instead, classical mechanics is now considered to be anapproximate theory to the more general quantum mechanics. Emphasis has shifted tounderstanding the fundamental forces of nature as in the Standard model and its more modernextensions into a unified theory of everything.[1] Classical mechanics is a theory for the study ofthe motion of non-quantum mechanical, low-energy particles in weak gravitational fields. In the21st century classical mechanics has been extended into the complex domain and complexclassical mechanics exhibits behaviors very similar to quantum mechanics.[2]Description of the theoryThe analysis of projectile motion is a part of classical mechanics.The following introduces the basic concepts of classical mechanics. For simplicity, it oftenmodels real-world objects as point particles, objects with negligible size. The motion of a pointparticle is characterized by a small number of parameters: its position, mass, and the forcesapplied to it. Each of these parameters is discussed in turn.In reality, the kind of objects that classical mechanics can describe always have a non-zero size.(The physics of very small particles, such as the electron, is more accurately described by
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quantum mechanics). Objects with non-zero size have more complicated behavior thanhypothetical point particles, because of the additional degrees of freedom—for example, abaseball can spin while it is moving. However, the results for point particles can be used to studysuch objects by treating them as composite objects, made up of a large number of interactingpoint particles. The center of mass of a composite object behaves like a point particle.Position and its derivativesMain article: Kinematics The SI derived "mechanical" (that is, not electromagnetic or thermal) units with kg, m and s position m angular position/angle unitless (radian) velocity m·s−1 angular velocity s−1 acceleration m·s−2 angular acceleration s−2 jerk m·s−3 "angular jerk" s−3 specific energy m2·s−2 absorbed dose rate m2·s−3 moment of inertia kg·m2 momentum kg·m·s−1 angular momentum kg·m2·s−1 force kg·m·s−2 torque kg·m2·s−2
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energy kg·m2·s−2 power kg·m2·s−3 pressure and energy density kg·m−1·s−2 surface tension kg·s−2 spring constant kg·s−2 irradiance and energy flux kg·s−3 kinematic viscosity m2·s−1 dynamic viscosity kg·m−1·s−1 density (mass density) kg·m−3 density (weight density) kg·m−2·s−2 number density m−3 action kg·m2·s−1The position of a point particle is defined with respect to an arbitrary fixed reference point, O, inspace, usually accompanied by a coordinate system, with the reference point located at the originof the coordinate system. It is defined as the vector r from O to the particle. In general, the pointparticle need not be stationary relative to O, so r is a function of t, the time elapsed since anarbitrary initial time. In pre-Einstein relativity (known as Galilean relativity), time is consideredan absolute, i.e., the time interval between any given pair of events is the same for all observers.In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for thestructure of space.[3]Velocity and speedMain articles: Velocity and speedThe velocity, or the rate of change of position with time, is defined as the derivative of theposition with respect to time or .
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In classical mechanics, velocities are directly additive and subtractive. For example, if one cartraveling east at 60 km/h passes another car traveling east at 50 km/h, then from the perspectiveof the slower car, the faster car is traveling east at 60 − 50 = 10 km/h. Whereas, from theperspective of the faster car, the slower car is moving 10 km/h to the west. Velocities are directlyadditive as vector quantities; they must be dealt with using vector analysis.Mathematically, if the velocity of the first object in the previous discussion is denoted by thevector u = ud and the velocity of the second object by the vector v = ve, where u is the speed ofthe first object, v is the speed of the second object, and d and e are unit vectors in the directionsof motion of each particle respectively, then the velocity of the first object as seen by the secondobject isSimilarly,When both objects are moving in the same direction, this equation can be simplified toOr, by ignoring direction, the difference can be given in terms of speed only:AccelerationMain article: AccelerationThe acceleration, or rate of change of velocity, is the derivative of the velocity with respect totime (the second derivative of the position with respect to time) orAcceleration can arise from a change with time of the magnitude of the velocity or of thedirection of the velocity or both. If only the magnitude v of the velocity decreases, this issometimes referred to as deceleration, but generally any change in the velocity with time,including deceleration, is simply referred to as acceleration.Frames of referenceMain articles: Inertial frame of reference and Galilean transformation
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While the position and velocity and acceleration of a particle can be referred to any observer inany state of motion, classical mechanics assumes the existence of a special family of referenceframes in terms of which the mechanical laws of nature take a comparatively simple form. Thesespecial reference frames are called inertial frames. An inertial frame is such that when an objectwithout any force interactions (an idealized situation) is viewed from it, it will appear either to beat rest or in a state of uniform motion in a straight line. This is the fundamental definition of aninertial frame. They are characterized by the requirement that all forces entering the observersphysical laws originate in identifiable sources (charges, gravitational bodies, and so forth). Anon-inertial reference frame is one accelerating with respect to an inertial one, and in such a non-inertial frame a particle is subject to acceleration by fictitious forces that enter the equations ofmotion solely as a result of its accelerated motion, and do not originate in identifiable sources.These fictitious forces are in addition to the real forces recognized in an inertial frame. A keyconcept of inertial frames is the method for identifying them. For practical purposes, referenceframes that are unaccelerated with respect to the distant stars are regarded as goodapproximations to inertial frames.Consider two reference frames S and S. For observers in each of the reference frames an eventhas space-time coordinates of (x,y,z,t) in frame S and (x,y,z,t) in frame S. Assuming time ismeasured the same in all reference frames, and if we require x = x when t = 0, then the relationbetween the space-time coordinates of the same event observed from the reference frames S andS, which are moving at a relative velocity of u in the x direction is: x = x − u·t y = y z = z t = t.This set of formulas defines a group transformation known as the Galilean transformation(informally, the Galilean transform). This group is a limiting case of the Poincaré group used inspecial relativity. The limiting case applies when the velocity u is very small compared to c, thespeed of light.The transformations have the following consequences: v′ = v − u (the velocity v′ of a particle from the perspective of S′ is slower by u than its velocity v from the perspective of S) a′ = a (the acceleration of a particle is the same in any inertial reference frame) F′ = F (the force on a particle is the same in any inertial reference frame) the speed of light is not a constant in classical mechanics, nor does the special position given to the speed of light in relativistic mechanics have a counterpart in classical mechanics.For some problems, it is convenient to use rotating coordinates (reference frames). Thereby onecan either keep a mapping to a convenient inertial frame, or introduce additionally a fictitiouscentrifugal force and Coriolis force.
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Forces; Newtons second lawMain articles: Force and Newtons laws of motionNewton was the first to mathematically express the relationship between force and momentum.Some physicists interpret Newtons second law of motion as a definition of force and mass, whileothers consider it to be a fundamental postulate, a law of nature. Either interpretation has thesame mathematical consequences, historically known as "Newtons Second Law":The quantity mv is called the (canonical) momentum. The net force on a particle is thus equal torate of change of momentum of the particle with time. Since the definition of acceleration is a =dv/dt, the second law can be written in the simplified and more familiar form:So long as the force acting on a particle is known, Newtons second law is sufficient to describethe motion of a particle. Once independent relations for each force acting on a particle areavailable, they can be substituted into Newtons second law to obtain an ordinary differentialequation, which is called the equation of motion.As an example, assume that friction is the only force acting on the particle, and that it may bemodeled as a function of the velocity of the particle, for example:where λ is a positive constant. Then the equation of motion isThis can be integrated to obtainwhere v0 is the initial velocity. This means that the velocity of this particle decays exponentiallyto zero as time progresses. In this case, an equivalent viewpoint is that the kinetic energy of theparticle is absorbed by friction (which converts it to heat energy in accordance with theconservation of energy), slowing it down. This expression can be further integrated to obtain theposition r of the particle as a function of time.Important forces include the gravitational force and the Lorentz force for electromagnetism. Inaddition, Newtons third law can sometimes be used to deduce the forces acting on a particle: if it
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is known that particle A exerts a force F on another particle B, it follows that B must exert anequal and opposite reaction force, −F, on A. The strong form of Newtons third law requires thatF and −F act along the line connecting A and B, while the weak form does not. Illustrations ofthe weak form of Newtons third law are often found for magnetic forces.Work and energyMain articles: Work (physics), kinetic energy, and potential energyIf a constant force F is applied to a particle that achieves a displacement Δr,[note 2] the work doneby the force is defined as the scalar product of the force and displacement vectors:More generally, if the force varies as a function of position as the particle moves from r1 to r2along a path C, the work done on the particle is given by the line integralIf the work done in moving the particle from r1 to r2 is the same no matter what path is taken, theforce is said to be conservative. Gravity is a conservative force, as is the force due to an idealizedspring, as given by Hookes law. The force due to friction is non-conservative.The kinetic energy Ek of a particle of mass m travelling at speed v is given byFor extended objects composed of many particles, the kinetic energy of the composite body isthe sum of the kinetic energies of the particles.The work–energy theorem states that for a particle of constant mass m the total work W done onthe particle from position r1 to r2 is equal to the change in kinetic energy Ek of the particle:Conservative forces can be expressed as the gradient of a scalar function, known as the potentialenergy and denoted Ep:If all the forces acting on a particle are conservative, and Ep is the total potential energy (which isdefined as a work of involved forces to rearrange mutual positions of bodies), obtained bysumming the potential energies corresponding to each force
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This result is known as conservation of energy and states that the total energy,is constant in time. It is often useful, because many commonly encountered forces areconservative.Beyond Newtons lawsClassical mechanics also includes descriptions of the complex motions of extended non-pointlikeobjects. Eulers laws provide extensions to Newtons laws in this area. The concepts of angularmomentum rely on the same calculus used to describe one-dimensional motion. The rocketequation extends the notion of rate of change of an objects momentum to include the effects ofan object "losing mass".There are two important alternative formulations of classical mechanics: Lagrangian mechanicsand Hamiltonian mechanics. These, and other modern formulations, usually bypass the conceptof "force", instead referring to other physical quantities, such as energy, for describingmechanical systems.The expressions given above for momentum and kinetic energy are only valid when there is nosignificant electromagnetic contribution. In electromagnetism, Newtons second law for current-carrying wires breaks down unless one includes the electromagnetic field contribution to themomentum of the system as expressed by the Poynting vector divided by c2, where c is the speedof light in free space.Limits of validity
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Domain of validity for Classical MechanicsMany branches of classical mechanics are simplifications or approximations of more accurateforms; two of the most accurate being general relativity and relativistic statistical mechanics.Geometric optics is an approximation to the quantum theory of light, and does not have asuperior "classical" form.The Newtonian approximation to special relativityIn special relativity, the momentum of a particle is given bywhere m is the particles mass, v its velocity, and c is the speed of light.If v is very small compared to c, v2/c2 is approximately zero, and soThus the Newtonian equation p = mv is an approximation of the relativistic equation for bodiesmoving with low speeds compared to the speed of light.For example, the relativistic cyclotron frequency of a cyclotron, gyrotron, or high voltagemagnetron is given by
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where fc is the classical frequency of an electron (or other charged particle) with kinetic energy Tand (rest) mass m0 circling in a magnetic field. The (rest) mass of an electron is 511 keV. So thefrequency correction is 1% for a magnetic vacuum tube with a 5.11 kV direct currentaccelerating voltage.The classical approximation to quantum mechanicsThe ray approximation of classical mechanics breaks down when the de Broglie wavelength isnot much smaller than other dimensions of the system. For non-relativistic particles, thiswavelength iswhere h is Plancks constant and p is the momentum.Again, this happens with electrons before it happens with heavier particles. For example, theelectrons used by Clinton Davisson and Lester Germer in 1927, accelerated by 54 volts, had awavelength of 0.167 nm, which was long enough to exhibit a single diffraction side lobe whenreflecting from the face of a nickel crystal with atomic spacing of 0.215 nm. With a largervacuum chamber, it would seem relatively easy to increase the angular resolution from around aradian to a milliradian and see quantum diffraction from the periodic patterns of integratedcircuit computer memory.More practical examples of the failure of classical mechanics on an engineering scale areconduction by quantum tunneling in tunnel diodes and very narrow transistor gates in integratedcircuits.Classical mechanics is the same extreme high frequency approximation as geometric optics. It ismore often accurate because it describes particles and bodies with rest mass. These have moremomentum and therefore shorter De Broglie wavelengths than massless particles, such as light,with the same kinetic energies.Branches
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Branches of mechanicsClassical mechanics was traditionally divided into three main branches: Statics, the study of equilibrium and its relation to forces Dynamics, the study of motion and its relation to forces Kinematics, dealing with the implications of observed motions without regard for circumstances causing themAnother division is based on the choice of mathematical formalism: Newtonian mechanics Lagrangian mechanics Hamiltonian mechanicsAlternatively, a division can be made by region of application: Celestial mechanics, relating to stars, planets and other celestial bodies Continuum mechanics, for materials which are modelled as a continuum, e.g., solids and fluids (i.e., liquids and gases). Relativistic mechanics (i.e. including the special and general theories of relativity), for bodies whose speed is close to the speed of light. Statistical mechanics, which provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk thermodynamic properties of materials.See also
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Ten Different Types of ForcesBy Erin Grady, eHow Contributor The magnetic force that attractsthese paper clips is just one kind of force.A force is an influence that causes physical change. There are ten basic kinds of forces: applied,gravitational, normal, friction, air resistance, tension, spring, electrical, magnetic and upthrust.Each of these forces does something different: some pull and some push, while others cause anobject to change form.Other People Are Reading The Difference Between Balanced & Unbalanced Force Ten Different Types of Levers Print this article 1. Applied Force o Applied force is transferred from a person or object to another person or object. If a man is pushing his chair across a room, he is using applied force on the chair. Gravitational Force
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o Large objects have a gravitational force, which attracts smaller objects. The best example of a gravitational force is the Earths interaction with people, animals and objects. Even the moon is pulled toward the Earth by a gravitational force. o Sponsored Links MRI Coils NewSales Repair 24 Hr Coil Repair & New GE Designs GE Siemens Hitachi &All OEM LowCost www.scanmed.comNormal Force o Normal force is exerted on an object when it is in contact with another object. When a coffee cup is resting on a table, the table is exerting a normal upward force on the cup to support its weight.Friction Force o Friction occurs when an object moves -- or tries to move -- across a surface and the surface opposes the objects movement. The amount of friction that is generated depends on how strongly the two surfaces are being pushed together and the nature of the surfaces. For example, pushing a book across a glassy surface will not create much friction, while sliding your feet across carpet will produce more friction.Air Resistance Force o Air resistance acts on objects as they travel through the air. This force will oppose motion, but only factors in when objects travel at high speeds or have a large surface area. For example, air resistance is smaller on a notebook falling from the desk than a kite falling from a tree.Tension Force o Tension passes through strings, cables, ropes or wires when they are being pulled in opposite directions. The tension force is directed along the length of the wire and pulls equally on objects at opposite ends of the string, cable, rope or wire.Spring Force o Spring force is exerted when a compressed or stretched spring is trying to return to an inert state. The string always wants to return to equilibrium and will do what it can to do so.
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Electrical Force o Electrical force is an attraction between positively and negatively charged objects. The closer the objects are to each other, the higher the electrical force. Magnetic Force o Magnetic force is an attraction force usually associated with electrical currents and magnets. Magnetic force attracts opposite forces. Each magnet has a north and a south end, each of which attracts the opposite ends of another magnet. For example, a north magnetic end will attract a south magnetic end, and vice versa. North ends of magnets repel each other, and vice versa. Magnets also create an attractive force with certain metals. Upthrust Force o Upthrust is more commonly known as buoyancy. This is the upward thrust that is caused by fluid pressure on objects, such as the pressure that allows boats to float.Read more: Ten Different Types of Forces | eHow.com http://www.ehow.com/list_7459343_ten-different-types-forces.html#ixzz2CfShdh8dAverage powerAs a simple example, burning a kilogram of coal releases much more energy than doesdetonating a kilogram of TNT,[3] but because the TNT reaction releases energy much morequickly, it delivers far more power than the coal. If ΔW is the amount of work performed duringa period of time of duration Δt, the average power Pavg over that period is given by the formulaIt is the average amount of work done or energy converted per unit of time. The average power isoften simply called "power" when the context makes it clear.The instantaneous power is then the limiting value of the average power as the time interval Δtapproaches zero.
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In the case of constant power P, the amount of work performed during a period of duration T isgiven by:In the context of energy conversion it is more customary to use the symbol E rather than W.Mechanical powerPower in mechanical systems is the combination of forces and movement. In particular, power isthe product of a force on an object and the objects velocity, or the product of a torque on a shaftand the shafts angular velocity.Mechanical power is also described as the time derivative of work. In mechanics, the work doneby a force F on an object that travels along a curve C is given by the line integral:where x defines the path C and v is the velocity along this path. The time derivative of theequation for work yields the instantaneous power,In rotational systems, power is the product of the torque τ and angular velocity ω,where ω measured in radians per second.In fluid power systems such as hydraulic actuators, power is given bywhere p is pressure in pascals, or N/m2 and Q is volumetric flow rate in m3/s in SI units.Mechanical advantageIf a mechanical system has no losses then the input power must equal the output power. Thisprovides a simple formula for the mechanical advantage of the system.Let the input power to a device be a force FA acting on a point that moves with velocity vA andthe output power be a force FB acts on a point that moves with velocity vB. If there are no lossesin the system, then
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and the mechanical advantage of the system is given byA similar relationship is obtained for rotating systems, where TA and ωA are the torque andangular velocity of the input and TB and ωB are the torque and angular velocity of the output. Ifthere are no losses in the system, thenwhich yields the mechanical advantageThese relations are important because they define the maximum performance of a device interms of velocity ratios determined by its physical dimensions. See for example gear ratios.Power in opticsIn optics, or radiometry, the term power sometimes refers to radiant flux, the average rate ofenergy transport by electromagnetic radiation, measured in watts. In other contexts, it refers tooptical power, the ability of a lens or other optical device to focus light. It is measured in dioptres(inverse metres), and equals the inverse of the focal length of the optical device.Electrical powerMain article: Electric powerThe instantaneous electrical power P delivered to a component is given bywhere P(t) is the instantaneous power, measured in watts (joules per second) V(t) is the potential difference (or voltage drop) across the component, measured in volts I(t) is the current through it, measured in amperesIf the component is a resistor with time-invariant voltage to current ratio, then:
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whereis the resistance, measured in ohms.Peak power and duty cycleIn a train of identical pulses, the instantaneous power is a periodic function of time. The ratio ofthe pulse duration to the period is equal to the ratio of the average power to the peak power. It isalso called the duty cycle (see text for definitions).In the case of a periodic signal of period , like a train of identical pulses, theinstantaneous power is also a periodic function of period . The peak power issimply defined by: .The peak power is not always readily measurable, however, and the measurement of the averagepower is more commonly performed by an instrument. If one defines the energy per pulseas:
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then the average power is: .One may define the pulse length such that so that the ratiosare equal. These ratios are called the duty cycle of the pulse train.A free body diagram, also called a force diagram,[1] is a pictorial representationoften used by physicists and engineers to analyze the forces acting on a body ofinterest. A free body diagram shows all forces of all types acting on this body.Drawing such a diagram can aid in solving for the unknown forces or theequations of motion of the body. Creating a free body diagram can make it easierto understand the forces, and torques or moments, in relation to one another andsuggest the proper concepts to apply in order to find the solution to a problem.The diagrams are also used as a conceptual device to help identify the internalforces—for example, shear forces and bending moments in beams—which aredeveloped within structures.[2][3] Number of sidesPolygons are primarily classified by the number of sides. See table below.Convexity and types of non-convexityPolygons may be characterized by their convexity or type of non-convexity: Convex: any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice. Equivalently, all its interior angles are less than 180°. Non-convex: a line may be found which meets its boundary more than twice. In other words, it contains at least one interior angle with a measure larger than 180°. Simple: the boundary of the polygon does not cross itself. All convex polygons are simple. Concave: Non-convex and simple. Star-shaped: the whole interior is visible from a single point, without crossing any edge. The polygon must be simple, and may be convex or concave. Self-intersecting: the boundary of the polygon crosses itself. Branko Grünbaum calls these coptic, though this term does not seem to be widely used. The term complex is
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sometimes used in contrast to simple, but this risks confusion with the idea of a complex polygon as one which exists in the complex Hilbert plane consisting of two complex dimensions. Star polygon: a polygon which self-intersects in a regular way.Symmetry Equiangular: all its corner angles are equal. Cyclic: all corners lie on a single circle. Isogonal or vertex-transitive: all corners lie within the same symmetry orbit. The polygon is also cyclic and equiangular. Equilateral: all edges are of the same length. (A polygon with 5 or more sides can be equilateral without being convex.) [1] Isotoxal or edge-transitive: all sides lie within the same symmetry orbit. The polygon is also equilateral. Tangential: all sides are tangent to an inscribed circle. Regular: A polygon is regular if it is both cyclic and equilateral. A non-convex regular polygon is called a regular star polygon.Miscellaneous Rectilinear: a polygon whose sides meet at right angles, i.e., all its interior angles are 90 or 270 degrees. Monotone with respect to a given line L, if every line orthogonal to L intersects the polygon not more than twice.PropertiesEuclidean geometry is assumed throughout.AnglesAny polygon, regular or irregular, self-intersecting or simple, has as many corners as it has sides.Each corner has several angles. The two most important ones are: Interior angle – The sum of the interior angles of a simple n-gon is (n − 2)π radians or (n − 2)180 degrees. This is because any simple n-gon can be considered to be made up of (n − 2) triangles, each of which has an angle sum of π radians or 180 degrees. The measure of any interior angle of a convex regular n-gon is radians or degrees. The interior angles of regular star polygons were first studied by Poinsot, in the same paper in which he describes the four regular star polyhedra. Exterior angle – Tracing around a convex n-gon, the angle "turned" at a corner is the exterior or external angle. Tracing all the way around the polygon makes one full turn, so the sum of the exterior angles must be 360°. This argument can be generalized to concave
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simple polygons, if external angles that turn in the opposite direction are subtracted from the total turned. Tracing around an n-gon in general, the sum of the exterior angles (the total amount one rotates at the vertices) can be any integer multiple d of 360°, e.g. 720° for a pentagram and 0° for an angular "eight", where d is the density or starriness of the polygon. See also orbit (dynamics).The exterior angle is the supplementary angle to the interior angle. From this the sum of theinterior angles can be easily confirmed, even if some interior angles are more than 180°: goingclockwise around, it means that one sometime turns left instead of right, which is counted asturning a negative amount. (Thus we consider something like the winding number of theorientation of the sides, where at every vertex the contribution is between −1⁄2 and 1⁄2 winding.)Area and centroidNomenclature of a 2D polygon.The area of a polygon is the measurement of the 2-dimensional region enclosed by the polygon.For a non-self-intersecting (simple) polygon with n vertices, the area and centroid are given by:[2]To close the polygon, the first and last vertices are the same, i.e., xn, yn = x0, y0. The vertices mustbe ordered according to positive or negative orientation (counterclockwise or clockwise,respectively); if they are ordered negatively, the value given by the area formula will be negativebut correct in absolute value. This is commonly called the Surveyors Formula.[3]The area formula is derived by taking each edge AB, and calculating the (signed) area of triangleABO with a vertex at the origin O, by taking the cross-product (which gives the area of aparallelogram) and dividing by 2. As one wraps around the polygon, these triangles with positiveand negative area will overlap, and the areas between the origin and the polygon will becancelled out and sum to 0, while only the area inside the reference triangle remains. This is whythe formula is called the Surveyors Formula, since the "surveyor" is at the origin; if going
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counterclockwise, positive area is added when going from left to right and negative area is addedwhen going from right to left, from the perspective of the origin.The formula was described by Meister[citation needed] in 1769 and by Gauss in 1795. It can beverified by dividing the polygon into triangles, but it can also be seen as a special case of Greenstheorem.The area A of a simple polygon can also be computed if the lengths of the sides, a1, a2, ..., an andthe exterior angles, θ1, θ2, ..., θn are known. The formula isThe formula was described by Lopshits in 1963.[4]If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points,Picks theorem gives a simple formula for the polygons area based on the numbers of interiorand boundary grid points.In every polygon with perimeter p and area A , the isoperimetric inequality holds.[5]If any two simple polygons of equal area are given, then the first can be cut into polygonal pieceswhich can be reassembled to form the second polygon. This is the Bolyai-Gerwien theorem.The area of a regular polygon is also given in terms of the radius r of its inscribed circle and itsperimeter p by .This radius is also termed its apothem and is often represented as a.The area of a regular n-gon with side s inscribed in a unit circle is .The area of a regular n-gon in terms of the radius r of its circumscribed circle and its perimeter pis given by .
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The area of a regular n-gon, inscribed in a unit-radius circle, with side s and interior angle θ canalso be expressed trigonometrically as .The sides of a polygon do not in general determine the area.[6] However, if the polygon is cyclicthe sides do determine the area. Of all n-gons with given sides, the one with the largest area iscyclic. Of all n-gons with a given perimeter, the one with the largest area is regular (andtherefore cyclic).[7]Self-intersecting polygonsThe area of a self-intersecting polygon can be defined in two different ways, each of which givesa different answer: Using the above methods for simple polygons, we discover that particular regions within the polygon may have their area multiplied by a factor which we call the density of the region. For example the central convex pentagon in the center of a pentagram has density 2. The two triangular regions of a cross-quadrilateral (like a figure 8) have opposite- signed densities, and adding their areas together can give a total area of zero for the whole figure. Considering the enclosed regions as point sets, we can find the area of the enclosed point set. This corresponds to the area of the plane covered by the polygon, or to the area of a simple polygon having the same outline as the self-intersecting one (or, in the case of the cross-quadrilateral, the two simple triangles).Degrees of freedomAn n-gon has 2n degrees of freedom, including 2 for position, 1 for rotational orientation, and 1for overall size, so 2n − 4 for shape. In the case of a line of symmetry the latter reduces to n − 2.Let k ≥ 2. For an nk-gon with k-fold rotational symmetry (Ck), there are 2n − 2 degrees offreedom for the shape. With additional mirror-image symmetry (Dk) there are n − 1 degrees offreedom.Product of distances from a vertex to other vertices of a regular polygonFor a regular n-gon inscribed in a unit-radius circle, the product of the distances from a givenvertex to all other vertices equals n.Generalizations of polygons
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In a broad sense, a polygon is an unbounded (without ends) sequence or circuit of alternatingsegments (sides) and angles (corners). An ordinary polygon is unbounded because the sequencecloses back in itself in a loop or circuit, while an apeirogon (infinite polygon) is unboundedbecause it goes on for ever so you can never reach any bounding end point. The modernmathematical understanding is to describe such a structural sequence in terms of an "abstract"polygon which is a partially ordered set (poset) of elements. The interior (body) of the polygon isanother element, and (for technical reasons) so is the null polytope or nullitope.A geometric polygon is understood to be a "realization" of the associated abstract polygon; thisinvolves some "mapping" of elements from the abstract to the geometric. Such a polygon doesnot have to lie in a plane, or have straight sides, or enclose an area, and individual elements canoverlap or even coincide. For example a spherical polygon is drawn on the surface of a sphere,and its sides are arcs of great circles. So when we talk about "polygons" we must be careful toexplain what kind we are talking about.A digon is a closed polygon having two sides and two corners. On the sphere, we can mark twoopposing points (like the North and South poles) and join them by half a great circle. Addanother arc of a different great circle and you have a digon. Tile the sphere with digons and youhave a polyhedron called a hosohedron. Take just one great circle instead, run it all the wayaround, and add just one "corner" point, and you have a monogon or henagon – although manyauthorities do not regard this as a proper polygon.Other realizations of these polygons are possible on other surfaces, but in the Euclidean (flat)plane, their bodies cannot be sensibly realized and we think of them as degenerate.The idea of a polygon has been generalized in various ways. Here is a short list of somedegenerate cases (or special cases, depending on your point of view): Digon: Interior angle of 0° in the Euclidean plane. See remarks above re. on the sphere. Interior angle of 180°: In the plane this gives an apeirogon (see below), on the sphere a dihedron A skew polygon does not lie in a flat plane, but zigzags in three (or more) dimensions. The Petrie polygons of the regular polyhedra are classic examples. A spherical polygon is a circuit of sides and corners on the surface of a sphere. An apeirogon is an infinite sequence of sides and angles, which is not closed but it has no ends because it extends infinitely. A complex polygon is a figure analogous to an ordinary polygon, which exists in the complex Hilbert plane.Naming polygonsThe word "polygon" comes from Late Latin polygōnum (a noun), from Greek πολύγωνον(polygōnon/polugōnon), noun use of neuter of πολύγωνος (polygōnos/polugōnos, the masculineadjective), meaning "many-angled". Individual polygons are named (and sometimes classified)according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral or quadrangle, and nonagon are
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exceptions. For large numbers, mathematicians usually write the numeral itself, e.g. 17-gon. Avariable can even be used, usually n-gon. This is useful if the number of sides is used in aformula.Some special polygons also have their own names; for example the regular star pentagon is alsoknown as the pentagram. Polygon names Name Edges Remarkshenagon (or In the Euclidean plane, degenerates to a closed curve with a 1monogon) single vertex point on it. In the Euclidean plane, degenerates to a closed curve with twodigon 2 vertex points on it.triangle (or trigon) 3 The simplest polygon which can exist in the Euclidean plane.quadrilateral (orquadrangle or 4 The simplest polygon which can cross itself.tetragon) The simplest polygon which can exist as a regular star. A starpentagon 5 pentagon is known as a pentagram or pentacle.hexagon 6 Avoid "sexagon" = Latin [sex-] + Greek. Avoid "septagon" = Latin [sept-] + Greek. The simplest polygon such that the regular form is not constructible withheptagon 7 compass and straightedge. However, it can be constructed using a Neusis construction.octagon 8 "Nonagon" is commonly used but mixes Latin [novem = 9]enneagon or nonagon 9 with Greek. Some modern authors prefer "enneagon", which is pure Greek.decagon 10 Avoid "undecagon" = Latin [un-] + Greek. The simplesthendecagon 11 polygon such that the regular form cannot be constructed with compass, straightedge, and angle trisector.dodecagon 12 Avoid "duodecagon" = Latin [duo-] + Greek.tridecagon (or 13triskaidecagon)tetradecagon (or 14tetrakaidecagon)pentadecagon (orquindecagon or 15pentakaidecagon)hexadecagon (or 16hexakaidecagon)
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heptadecagon (or 17heptakaidecagon)octadecagon (or 18octakaidecagon)enneadecagon (orenneakaidecagon or 19nonadecagon)icosagon 20triacontagon 30 "hectogon" is the Greek name (see hectometer), "centagon" is ahectogon 100 Latin-Greek hybrid; neither is widely attested. René Descartes,[8] Immanuel Kant,[9] David Hume, [10] andchiliagon 1000 others have used the chiliagon as an example in philosophical discussion.myriagon 10,000 As with René Descartes example of the chiliagon, the million- sided polygon has been used as an illustration of a well-definedmegagon[11][12][13] 1,000,000 concept that cannot be visualised.[14][15][16][17][18][19][20] The megagon is also used as an illustration of the convergence of regular polygons to a circle.[21]apeirogon A degenerate polygon of infinitely many sidesConstructing higher namesTo construct the name of a polygon with more than 20 and less than 100 edges, combine theprefixes as follows and Ones final suffix Tens 1 -hena-20 icosa- 2 -di-30 triaconta- 3 -tri-40 tetraconta- 4 -tetra-50 pentaconta- -kai- 5 -penta- -gon60 hexaconta- 6 -hexa-70 heptaconta- 7 -hepta-80 octaconta- 8 -octa-90 enneaconta- 9 -ennea-The "kai" is not always used. Opinions differ on exactly when it should, or need not, be used (seealso examples above).
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Alternatively, the system used for naming the higher alkanes (completely saturatedhydrocarbons) can be used: Ones Tens final suffix1 hen- 10 deca-2 do- 20 -cosa-3 tri- 30 triaconta-4 tetra- 40 tetraconta-5 penta- 50 pentaconta- -gon6 hexa- 60 hexaconta-7 hepta- 70 heptaconta-8 octa- 80 octaconta-9 ennea- (or nona-) 90 enneaconta- (or nonaconta-)This has the advantage of being consistent with the system used for 10- through 19-sided figures.That is, a 42-sided figure would be named as follows:Ones Tens final suffix full polygon namedo- tetraconta- -gon dotetracontagonand a 50-sided figure Tens and Ones final suffix full polygon namepentaconta- -gon pentacontagonBut beyond enneagons and decagons, professional mathematicians generally prefer theaforementioned numeral notation (for example, MathWorld has articles on 17-gons and 257-gons). Exceptions exist for side counts that are more easily expressed in verbal form.HistoryThe component method is the concept that you can resolve vectors into twoindependent (therefore perpendicular) vectors (say, in the x and y directions).And, you can "put a vector back together" simply, using the distance formulaand the slope of the line.So, the component form and the direction/magnitude forms are just two differentways of specifying a vector. he Component Method for Vector Addition andScalar Multiplication
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When we mentioned in the introduction that a vector is either an ordered pair or a triplet ofnumbers we implicitly defined vectors in terms of components.Each entry in the 2-dimensional ordered pair (a, b) or 3-dimensional triplet (a, b, c) is called acomponent of the vector. Unless otherwise specified, it is normally understood that the entriescorrespond to the number of units the vector has in the x , y , and (for the 3D case) z directions ofa plane or space. In other words, you can think of the components as simply the coordinates ofthe point associated with the vector. (In some sense, the vector is the point, although when wedraw vectors we normally draw an arrow from the origin to the point.) Figure %: The vector (a, b) in the Euclidean plane.Vector Addition Using ComponentsGiven two vectors u = (u 1, u 2) and v = (v 1, v 2) in the Euclidean plane, the sum is given by: u + v = (u 1 + v 1, u 2 + v 2)For three-dimensional vectors u = (u 1, u 2, u 3) and v = (v 1, v 2, v 3) , the formula is almostidentical: u + v = (u 1 + v 1, u 2 + v 2, u 3 + v 3)In other words, vector addition is just like ordinary addition: component by component.Notice that if you add together two 2-dimensional vectors you must get another 2-dimensionalvector as your answer. Addition of 3-dimensional vectors will yield 3-dimensional answers. 2-and 3-dimensional vectors belong to different vector spaces and cannot be added. These samerules apply when we are dealing with scalar multiplication.Scalar Multiplication of Vectors Using Components
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Given a single vector v = (v 1, v 2) in the Euclidean plane, and a scalar a (which is a real number),the multiplication of the vector by the scalar is defined as: av = (av 1, av 2)Similarly, for a 3-dimensional vector v = (v 1, v 2, v 3) and a scalar a , the formula for scalarmultiplication is: av = (av 1, av 2, av 3)So what we are doing when we multiply a vector by a scalar a is obtaining a new vector (of thesame dimension) by multiplying each component of the original vector by a .Unit VectorsFor 3-dimensional vectors, it is often customary to define unit vectors pointing in the x , y , and zdirections. These vectors are usually denoted by the letters i , j , and k , respectively, and all havelength 1 . Thus, i = (1, 0, 0) , j = (0, 1, 0) , and k = (0, 0, 1) . This enables us to write a vector asa sum in the following way: (a, b, c) = a(1, 0, 0) + b(0, 1, 0) + c(0, 0, 1) =a i + b j + c kVector SubtractionSubtraction for vectors (as with ordinary numbers) is not a new operation. If you want to performthe vector subtraction u - v , you simply use the rules for vector addition and scalarmultiplication: u - v = u + (- 1)v .In the next section, we will see how these rules for addition and scalar multiplication of vectorscan be understood in a geometric way. We will find, for instance, that vector addition can bedone graphically (i.e. without even knowing the components of the vectors involved), and thatscalar multiplication of a vector amounts to a change in the vectors magnitude, but does not alterits direction.Resultant force refers to the reduction of a system of forces acting on a body to a single forceand an associated torque. The choice of the point of application of the force determines the
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associated torque.[1] The term resultant force should be understood to refer to both the forces andtorques acting on a rigid body, which is why some use the term resultant force-torque.The resultant force, or resultant force-torque, fully replaces the effects of all forces on the motionof the rigid body they act upon.Associated torqueIf a point R is selected as the point of application of the resultant force F of a system of n forcesFi then the associated torque T is determined from the formulasandIt is useful to note that the point of application R of the resultant force may be anywhere alongthe line of action of F without changing the value of the associated torque. To see this add thevector kF to the point of application R in the calculation of the associated torque,The right side of this equation can be separated into the original formula for T plus the additionalterm including kF,Now because F is the sum of the vectors Fi this additional term is zero, that isand the value of the associated torque is unchanged.Torque-free resultant
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it is useful to consider whether there is a point of application R such that the associated torque iszero. This point is defined by propertywhere F is resultant force and Fi form the system of forces.Notice that this equation for R has a solution only if the sum of the individual torques on theright side yield a vector that is perpendicular to F. Thus, the condition that a system of forces hasa torque-free resultant can be written asIf this condition is not satisfied, then the system of forces includes a pure torque.The diagram illustrates simple graphical methods for finding the line of application of theresultant force of simple planar systems. 1. Lines of application of the actual forces and on the leftmost illustration intersect. After vector addition is performed "at the location of ", the net force obtained is translated so that its line of application passes through the common intersection point. With respect to that point all torques are zero, so the torque of the resultant force is equal to the sum of the torques of the actual forces. 2. Illustration in the middle of the diagram shows two parallel actual forces. After vector addition "at the location of ", the net force is translated to the appropriate line of application, where it becomes the resultant force . The procedure is based on decomposition of all forces into components for which the lines of application (pale dotted lines) intersect at one point (the so called pole, arbitrarily set at the right side of the illustration). Then the arguments from the previous case are applied to the forces and their components to demonstrate the torque relationships. 3. The rightmost illustration shows a couple, two equal but opposite forces for which the amount of the net force is zero, but they produce the net torque where is the distance between their lines of application. This is "pure" torque, since there is no resultant force.WrenchThe forces and torques acting on a rigid body can be assembled into the pair of vectors called awrench.[2] Let P be the point of application of the force F and let R be the vector locating thispoint in a fixed frame. Then the pair of vectors W=(F, R×F) is called a wrench. Vectors of thisform are know as screws and their mathematics formulation is called screw theory.[3][4]
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The resultant force and torque on a rigid body obtained from a system of forces Fi i=1,...,n, issimply the sum of the individual wrenches Wi, that isNotice that the case of two equal but opposite forces F and -F acting at points A and Brespectively, yields the resultant W=(F-F, A×F - B× F) = (0, (A-B)×F). This shows thatwrenches of the form W=(0, T) can be interpreted as pure torques.What are the Main Branches of Natural ScienceNatural science involves the study of phenomena or laws of physical world. Following are thekey branches of natural science. Read on...Natural science can be defined as a rational approach to the study of the universe and thephysical world. Astronomy, biology, chemistry, earth science and physics are the main branchesof natural science. There are some cross-disciplines of natural science such as astrophysics,biophysics, physical chemistry, geochemistry, biochemistry, astrochemistry, etc.Astronomy deals with the scientific study of celestial bodies including stars, comets, planets andgalaxies and phenomena that originate outside the earths atmosphere such as the cosmicbackground radiation.Biology or biological science is the scientific study of living things, including the study of theirstructure, origin, growth, evolution, function and distribution. Different branches of biology arezoology, botany, genetics, ecology, marine biology and biochemistry.Chemistry is a branch of natural science that deals with the composition of substances as well astheir properties and reactions. It involves the study of matter and its interactions with energy anditself. Today, a number of disciplines exist under the various branches of chemistry.Earth science includes the study of the earths system in space that includes weather and climatesystems as well as the study of nonliving things such as oceans, rocks and planets. It deals withthe physical aspects of the earth, such as its formation, structure, and related phenomena. Itincludes different branches such as geology, geography, meteorology, oceanography andastronomy.Physics is a branch of natural science that is associated with the study of properties andinteractions of time, space, energy and matter.Read more at Buzzle: http://www.buzzle.com/articles/what-are-the-main-branches-of-natural-science.htmlIn physics, a scalar is a simple physical quantity that is unchanged by coordinate systemrotations or translations (in Newtonian mechanics), or by Lorentz transformations or central-timetranslations (in relativity). A scalar is a quantity which can be described by a single number,unlike vectors, tensors, etc. which are described by several numbers which describe magnitude
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and direction. A related concept is a pseudoscalar, which is invariant under proper rotations but(like a pseudovector) flips sign under improper rotations. The concept of a scalar in physics isessentially the same as in mathematics.An example of a scalar quantity is temperature; the temperature at a given point is a singlenumber. Velocity, for example, is a vector quantity. Velocity in four-dimensional space isspecified by three values; in a Cartesian coordinate system the values are the speeds relative toeach coordinate axis.Vector, a Latin word meaning "carrier",In mathematics,Direction is the information contained in the relative position of one point with respect to another pointwithout the distance information. Directions may be either relative to some indicated reference (theviolins in a full orchestra are typically seated to the left of the conductor), or absolute according to somepreviously agreed upon frame of reference (New York City lies due west of Madrid). Direction is oftenindicated manually by an extended index finger or written as an arrow. On a vertically oriented signrepresenting a horizontal plane, such as a road sign, "forward" is usually indicated by an upward arrow.Mathematically, direction may be uniquely specified by a unit vector, or equivalently by the angles madeby the most direct path with respect to a specified set of axes.magnitude is the "size" of a mathematical object, a property by which the object can be compared aslarger or smaller than other objects of the same kind. More formally, an objects magnitude is anordering (or ranking) of the class of objects to which it belongs.When referring to a two and three-dimensional plane, the x-axis or horizontal axis refers to thehorizontal width of a two or three-dimensional object. In the picture to the right, the x-axis plane goesleft-to-right and intersects with the y-axis and z-axis. A good example of where the x-axis is used on acomputer is with the mouse. By assigning a value to the x-axis, when the mouse is moved left-to-rightthe x-axis value increases and decreases, which allows the computer to know where the mouse cursor ison the screen.he vertical axis of a two-dimensional plot in Cartesian coordinates. Physicists and astronomerssometimes call this axis the ordinate, although that term is more commonly used to refer tocoordinates along the -axis. n physics, a force is any influence that causes an object to undergoa certain change, either concerning its movement, direction, or geometrical construction. It ismeasured with the SI unit of newtons and represented by the symbol F. In other words, a force isthat which can cause an object with mass to change its velocity (which includes to begin movingfrom a state of rest), i.e., to accelerate, or which can cause a flexible object to deform. Force canalso be described by intuitive concepts such as a push or pull. A force has both magnitude anddirection, making it a vector quantity.The original form of Newtons second law states that the net force acting upon an object is equalto the rate at which its momentum changes.[1] This law is further given to mean that theacceleration of an object is directly proportional to the net force acting on the object, is in the
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direction of the net force, and is inversely proportional the mass of the object. As a formula, thisis expressed as:where the arrows imply a vector quantity possessing both magnitude and direction.Related concepts to force include: thrust, which increases the velocity of an object; drag, whichdecreases the velocity of an object; and torque which produces changes in rotational speed of anobject. Forces which do not act uniformly on all parts of a body will also cause mechanicalstresses,[2] a technical term for influences which cause deformation of matter. While mechanicalstress can remain embedded in a solid object, gradually deforming it, mechanical stress in a fluiddetermines changes in its pressure and volume.[3][4]
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