Physics (from Ancient Greek: φύσις physis "nature") is a natural science that involves the study of matter [1] and its motion through space and time, along with related concepts such as energy and force.[2] More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.[3][4][5]

Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.[1] In an older and closely related meaning (found, for example, in Aristotle), "science" refers to the body of reliable knowledge itself, of the type that can be logically and rationally explained (see History and philosophy below).[2] Since classical antiquity science as a type of knowledge was closely linked to philosophy. In the early modern era the words "science" and "philosophy" were sometimes used interchangeably in the English language. By the 17th century, natural philosophy (which is today called "natural science") was considered a separate branch of philosophy.[3] However, "science" continued to be used in a broad sense denoting reliable knowledge about a topic, in the same way it is still used in modern terms such as library science or political science.

The branches of science (which are also referred to as "sciences", "scientific fields", or "scientific disciplines") are commonly divided into two major groups: natural sciences, which study natural phenomena (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 observable phenomena and capable of being tested for its validity by other researchers working under the same conditions.[1] There are also related disciplines that are grouped into interdisciplinary and applied sciences, such as engineering and medicine. Within these categories are specialized scientific fields that can include parts of other scientific disciplines but often possess their own terminology and expertise.[2]

PHYSICS

Physics is the science of matter and energy, and the movement and interactions between them both. 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

nuclear physics solid state physics plasma physics geophysics biophysics

The two main branches are : 1) Classical Mechanics 2) Quantum MechanicsThis article is about the physics 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]

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In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, 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 other specific sub-topics. Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to

introduce the other major sub-field of mechanics, quantum mechanics, which reconciles the macroscopic laws of physics with the atomic nature of matter and handles the wave–particle duality of atoms and molecules. In the case of high velocity objects approaching the speed of light, classical mechanics is enhanced by special relativity. General relativity unifies special relativity with Newton's law of universal gravitation, allowing physicists to handle gravitation at a deeper level.

The term classical mechanics was coined in the early 20th century to describe the system of physics 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 on the precise observations of Tycho Brahe and the studies of terrestrial projectile motion of Galileo. Since these aspects of physics were developed long before the emergence of quantum physics and relativity, some sources exclude Einstein's theory of relativity from this category. However, a number of modern sources do include relativistic mechanics, which in their view represents 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 Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by Newton himself, in parallel with Leibniz, and others. This is further described in the following sections. Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newton's work, particularly through their use of analytical mechanics. Ultimately, the mathematics developed for these were central to the creation of quantum 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; Newton's second law o 2.3 Work and energy o 2.4 Beyond Newton's 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

9 External links

History

Main article: History of classical mechanicsSee also: Timeline of classical mechanics

Classical Physics

Wave equation

History of physics

Founders[show]

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Scientists[show]

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Some 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 that theoretical principles can assist in the understanding of nature. While to a modern reader, many of these preserved ideas come forth as eminently reasonable, there is a conspicuous lack of both mathematical theory and controlled experiment, as we know it. These both turned out to be decisive 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 of Jordanus de Nemore. In the Elementa super demonstrationem ponderum, he introduces the concept of "positional gravity" and the use of component forces.

Three stage Theory of impetus according to Albert of Saxony.

The first published causal explanation of the motions of planets was Johannes Kepler's Astronomia nova published in 1609. He concluded, based on Tycho Brahe's observations of the orbit of Mars, that the orbits were ellipses. This break with ancient thought was happening around the same time that Galileo was proposing abstract mathematical laws for the motion of objects. He may (or may not) have performed the famous experiment of dropping two cannon balls of different weights from the tower of Pisa, showing that they both hit the ground at the same time. The reality of this experiment is disputed, but, more importantly, he did carry out quantitative experiments by rolling balls on an inclined plane. His theory of accelerated motion derived 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 three laws of motion form the basis of classical mechanics

As foundation for his principles of natural philosophy, Isaac Newton proposed three laws of motion: the law of inertia, his second law of acceleration (mentioned above), and the law of

action and reaction; and hence laid the foundations for classical mechanics. Both Newton's second and third laws were given proper scientific and mathematical treatment in Newton's Philosophiæ Naturalis Principia Mathematica, which distinguishes them from earlier attempts at explaining similar phenomena, which were either incomplete, incorrect, or given little accurate mathematical expression. Newton also enunciated the principles of conservation of momentum and angular momentum. In mechanics, Newton was also the first to provide the first correct scientific and mathematical formulation of gravity in Newton's law of universal gravitation. The combination of Newton's laws of motion and gravitation provide the fullest and most accurate description of classical mechanics. He demonstrated that these laws apply to everyday objects as well as to celestial objects. In particular, he obtained a theoretical explanation of Kepler's laws of motion of the planets.

Newton previously invented the calculus, of mathematics, and used it to perform the mathematical calculations. For acceptability, his book, the Principia, was formulated entirely in terms 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[citation

needed] today.

Hamilton's greatest contribution is perhaps the reformulation of Newtonian mechanics, now called Hamiltonian mechanics.

Newton, and most of his contemporaries, with the notable exception of Huygens, worked on the assumption that classical mechanics would be able to explain all phenomena, including light, in the form of geometric optics. Even when discovering the so-called Newton's rings (a wave interference 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 as physics. After Newton there were several re-formulations which progressively allowed a solution to be found to a far greater number of problems. The first notable re-formulation was in 1788 by Joseph Louis Lagrange. Lagrangian mechanics was in turn re-formulated in 1833 by William Rowan Hamilton.

Some difficulties were discovered in the late 19th century that could only be resolved by more modern physics. Some of these difficulties related to compatibility with electromagnetic theory,

and the famous Michelson–Morley experiment. The resolution of these problems led to the special theory of relativity, often included in the term classical mechanics.

A second set of difficulties were related to thermodynamics. When combined with thermodynamics, classical mechanics leads to the Gibbs paradox of classical statistical mechanics, in which entropy is not a well-defined quantity. Black-body radiation was not explained without the introduction of quanta. As experiments reached the atomic level, classical mechanics failed to explain, even approximately, such basic things as the energy levels and sizes of atoms and the photo-electric effect. The effort at resolving these problems led to the development of quantum mechanics.

Since the end of the 20th century, the place of classical mechanics in physics has been no longer that of an independent theory. Instead, classical mechanics is now considered to be an approximate theory to the more general quantum mechanics. Emphasis has shifted to understanding the fundamental forces of nature as in the Standard model and its more modern extensions into a unified theory of everything.[1] Classical mechanics is a theory for the study of the motion of non-quantum mechanical, low-energy particles in weak gravitational fields. In the 21st century classical mechanics has been extended into the complex domain and complex classical mechanics exhibits behaviors very similar to quantum mechanics.[2]

Description of the theory

The analysis of projectile motion is a part of classical mechanics.

The following introduces the basic concepts of classical mechanics. For simplicity, it often models real-world objects as point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied 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 quantum mechanics). Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a

baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle.

Position and its derivatives

Main article: KinematicsThe 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

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−1

The position of a point particle is defined with respect to an arbitrary fixed reference point, O, in space, usually accompanied by a coordinate system, with the reference point located at the origin of the coordinate system. It is defined as the vector r from O to the particle. In general, the point particle need not be stationary relative to O, so r is a function of t, the time elapsed since an arbitrary initial time. In pre-Einstein relativity (known as Galilean relativity), time is considered an 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 the structure of space.[3]

Velocity and speed

Main articles: Velocity and speed

The velocity, or the rate of change of position with time, is defined as the derivative of the position with respect to time or

.

In classical mechanics, velocities are directly additive and subtractive. For example, if one car traveling east at 60 km/h passes another car traveling east at 50 km/h, then from the perspective of the slower car, the faster car is traveling east at 60 − 50 = 10 km/h. Whereas, from the perspective of the faster car, the slower car is moving 10 km/h to the west. Velocities are directly additive 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 the vector u = ud and the velocity of the second object by the vector v = ve, where u is the speed of the first object, v is the speed of the second object, and d and e are unit vectors in the directions of motion of each particle respectively, then the velocity of the first object as seen by the second object is

Similarly,

When both objects are moving in the same direction, this equation can be simplified to

Or, by ignoring direction, the difference can be given in terms of speed only:

Acceleration

Main article: Acceleration

The acceleration, or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time) or

Acceleration can arise from a change with time of the magnitude of the velocity or of the direction of the velocity or both. If only the magnitude v of the velocity decreases, this is sometimes referred to as deceleration, but generally any change in the velocity with time, including deceleration, is simply referred to as acceleration.

Frames of reference

Main articles: Inertial frame of reference and Galilean transformation

While the position and velocity and acceleration of a particle can be referred to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in terms of which the mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames. An inertial frame is such that when an object without any force interactions (an idealized situation) is viewed from it, it will appear either to be at rest or in a state of uniform motion in a straight line. This is the fundamental definition of an inertial frame. They are characterized by the requirement that all forces entering the observer's

physical laws originate in identifiable sources (charges, gravitational bodies, and so forth). A non-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 of motion 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 key concept of inertial frames is the method for identifying them. For practical purposes, reference frames that are unaccelerated with respect to the distant stars are regarded as good approximations to inertial frames.

Consider two reference frames S and S'. For observers in each of the reference frames an event has space-time coordinates of (x,y,z,t) in frame S and (x',y',z',t') in frame S'. Assuming time is measured the same in all reference frames, and if we require x = x' when t = 0, then the relation between the space-time coordinates of the same event observed from the reference frames S' and S, which are moving at a relative velocity of u in the x direction is:

x' = x − u·ty' = yz' = zt' = 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 in special relativity. The limiting case applies when the velocity u is very small compared to c, the speed 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 one can either keep a mapping to a convenient inertial frame, or introduce additionally a fictitious centrifugal force and Coriolis force.

Forces; Newton's second law

Main articles: Force and Newton's laws of motion

Newton was the first to mathematically express the relationship between force and momentum. Some physicists interpret Newton's second law of motion as a definition of force and mass, while

others consider it to be a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law":

The quantity mv is called the (canonical) momentum. The net force on a particle is thus equal to rate 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, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, 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 be modeled as a function of the velocity of the particle, for example:

where λ is a positive constant. Then the equation of motion is

This can be integrated to obtain

where v0 is the initial velocity. This means that the velocity of this particle decays exponentially to zero as time progresses. In this case, an equivalent viewpoint is that the kinetic energy of the particle is absorbed by friction (which converts it to heat energy in accordance with the conservation of energy), slowing it down. This expression can be further integrated to obtain the position r of the particle as a function of time.

Important forces include the gravitational force and the Lorentz force for electromagnetism. In addition, Newton's third law can sometimes be used to deduce the forces acting on a particle: if it is known that particle A exerts a force F on another particle B, it follows that B must exert an equal and opposite reaction force, −F, on A. The strong form of Newton's third law requires that F and −F act along the line connecting A and B, while the weak form does not. Illustrations of the weak form of Newton's third law are often found for magnetic forces.

Work and energy

Main articles: Work (physics), kinetic energy, and potential energy

If a constant force F is applied to a particle that achieves a displacement Δr,[note 2] the work done by 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 r2 along a path C, the work done on the particle is given by the line integral

If the work done in moving the particle from r1 to r2 is the same no matter what path is taken, the force is said to be conservative. Gravity is a conservative force, as is the force due to an idealized spring, as given by Hooke's 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 by

For extended objects composed of many particles, the kinetic energy of the composite body is the 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 on the 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 potential energy and denoted Ep:

If all the forces acting on a particle are conservative, and Ep is the total potential energy (which is defined as a work of involved forces to rearrange mutual positions of bodies), obtained by summing the potential energies corresponding to each force

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 are conservative.

Beyond Newton's laws

Classical mechanics also includes descriptions of the complex motions of extended non-pointlike objects. Euler's laws provide extensions to Newton's laws in this area. The concepts of angular momentum rely on the same calculus used to describe one-dimensional motion. The rocket equation extends the notion of rate of change of an object's momentum to include the effects of an object "losing mass".

There are two important alternative formulations of classical mechanics: Lagrangian mechanics and Hamiltonian mechanics. These, and other modern formulations, usually bypass the concept of "force", instead referring to other physical quantities, such as energy, for describing mechanical systems.

The expressions given above for momentum and kinetic energy are only valid when there is no significant electromagnetic contribution. In electromagnetism, Newton's second law for current-carrying wires breaks down unless one includes the electromagnetic field contribution to the momentum of the system as expressed by the Poynting vector divided by c2, where c is the speed of light in free space.

Limits of validity

Domain of validity for Classical Mechanics

Many branches of classical mechanics are simplifications or approximations of more accurate forms; 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 a superior "classical" form.

The Newtonian approximation to special relativity

In special relativity, the momentum of a particle is given by

where m is the particle's 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 so

Thus the Newtonian equation p = mv is an approximation of the relativistic equation for bodies moving with low speeds compared to the speed of light.

For example, the relativistic cyclotron frequency of a cyclotron, gyrotron, or high voltage magnetron is given by

where fc is the classical frequency of an electron (or other charged particle) with kinetic energy T and (rest) mass m0 circling in a magnetic field. The (rest) mass of an electron is 511 keV. So the frequency correction is 1% for a magnetic vacuum tube with a 5.11 kV direct current accelerating voltage.

The classical approximation to quantum mechanics

The ray approximation of classical mechanics breaks down when the de Broglie wavelength is not much smaller than other dimensions of the system. For non-relativistic particles, this wavelength is

where h is Planck's constant and p is the momentum.

Again, this happens with electrons before it happens with heavier particles. For example, the electrons used by Clinton Davisson and Lester Germer in 1927, accelerated by 54 volts, had a wavelength of 0.167 nm, which was long enough to exhibit a single diffraction side lobe when reflecting from the face of a nickel crystal with atomic spacing of 0.215 nm. With a larger

vacuum chamber, it would seem relatively easy to increase the angular resolution from around a radian to a milliradian and see quantum diffraction from the periodic patterns of integrated circuit computer memory.

More practical examples of the failure of classical mechanics on an engineering scale are conduction by quantum tunneling in tunnel diodes and very narrow transistor gates in integrated circuits.

Classical mechanics is the same extreme high frequency approximation as geometric optics. It is more often accurate because it describes particles and bodies with rest mass. These have more momentum and therefore shorter De Broglie wavelengths than massless particles, such as light, with the same kinetic energies.

Branches

Branches of mechanics

Classical 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 them

Another division is based on the choice of mathematical formalism:

Newtonian mechanics Lagrangian mechanics Hamiltonian mechanics

Alternatively, 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

Ten Different Types of ForcesBy Erin Grady, eHow Contributor

The magnetic force that attracts these 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 an object to change form.

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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

o Large objects have a gravitational force, which attracts smaller objects. The best example of a gravitational force is the Earth's interaction with people, animals and objects. Even the moon is pulled toward the Earth by a gravitational force.

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Normal 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 object's 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.

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#ixzz2CfShdh8d

Average power

As a simple example, burning a kilogram of coal releases much more energy than does detonating a kilogram of TNT,[3] but because the TNT reaction releases energy much more quickly, it delivers far more power than the coal. If ΔW is the amount of work performed during a period of time of duration Δt, the average power Pavg over that period is given by the formula

It is the average amount of work done or energy converted per unit of time. The average power is often 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 Δt approaches zero.

In the case of constant power P, the amount of work performed during a period of duration T is given by:

In the context of energy conversion it is more customary to use the symbol E rather than W.

Mechanical power

Power in mechanical systems is the combination of forces and movement. In particular, power is the product of a force on an object and the object's velocity, or the product of a torque on a shaft and the shaft's angular velocity.

Mechanical power is also described as the time derivative of work. In mechanics, the work done by 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 the equation 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 by

where p is pressure in pascals, or N/m2 and Q is volumetric flow rate in m3/s in SI units.

Mechanical advantage

If a mechanical system has no losses then the input power must equal the output power. This provides 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 and the output power be a force FB acts on a point that moves with velocity vB. If there are no losses in the system, then

and the mechanical advantage of the system is given by

A similar relationship is obtained for rotating systems, where TA and ωA are the torque and angular velocity of the input and TB and ωB are the torque and angular velocity of the output. If there are no losses in the system, then

which yields the mechanical advantage

These relations are important because they define the maximum performance of a device in terms of velocity ratios determined by its physical dimensions. See for example gear ratios.

Power in optics

In optics, or radiometry, the term power sometimes refers to radiant flux, the average rate of energy transport by electromagnetic radiation, measured in watts. In other contexts, it refers to

optical 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 power

Main article: Electric power

The instantaneous electrical power P delivered to a component is given by

where

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 voltsI(t) is the current through it, measured in amperes

If the component is a resistor with time-invariant voltage to current ratio, then:

where

is the resistance, measured in ohms.

Peak power and duty cycle

In a train of identical pulses, the instantaneous power is a periodic function of time. The ratio of the pulse duration to the period is equal to the ratio of the average power to the peak power. It is also called the duty cycle (see text for definitions).

In the case of a periodic signal of period , like a train of identical pulses, the instantaneous

power is also a periodic function of period . The peak power is simply defined by:

.

The peak power is not always readily measurable, however, and the measurement of the average

power is more commonly performed by an instrument. If one defines the energy per pulse as:

then the average power is:

.

One may define the pulse length such that so that the ratios

are 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 representation often used by physicists and engineers to analyze the forces acting on a body of interest. 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 the equations of motion of the body. Creating a free body diagram can make it easier to understand the forces, and torques or moments, in relation to one another and suggest 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 internal forces—for example, shear forces and bending moments in beams—which are developed within structures.[2][3] Number of sides

Polygons are primarily classified by the number of sides. See table below.

Convexity and types of non-convexity

Polygons 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 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.

Properties

Euclidean geometry is assumed throughout.

Angles

Any 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 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 the interior angles can be easily confirmed, even if some interior angles are more than 180°: going clockwise around, it means that one sometime turns left instead of right, which is counted as turning a negative amount. (Thus we consider something like the winding number of the orientation of the sides, where at every vertex the contribution is between −1⁄2 and 1⁄2 winding.)

Area and centroid

Nomenclature 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 must be 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 negative but correct in absolute value. This is commonly called the Surveyor's Formula.[3]

The area formula is derived by taking each edge AB, and calculating the (signed) area of triangle ABO with a vertex at the origin O, by taking the cross-product (which gives the area of a parallelogram) and dividing by 2. As one wraps around the polygon, these triangles with positive and negative area will overlap, and the areas between the origin and the polygon will be cancelled out and sum to 0, while only the area inside the reference triangle remains. This is why the formula is called the Surveyor's Formula, since the "surveyor" is at the origin; if going counterclockwise, positive area is added when going from left to right and negative area is added when 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 be verified by dividing the polygon into triangles, but it can also be seen as a special case of Green's theorem.

The area A of a simple polygon can also be computed if the lengths of the sides, a1, a2, ..., an and the exterior angles, θ1, θ2, ..., θn are known. The formula is

The 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, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and 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 pieces which 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 its perimeter 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 p is given by

.

The area of a regular n-gon, inscribed in a unit-radius circle, with side s and interior angle θ can also be expressed trigonometrically as

.

The sides of a polygon do not in general determine the area.[6] However, if the polygon is cyclic the sides do determine the area. Of all n-gons with given sides, the one with the largest area is

cyclic. Of all n-gons with a given perimeter, the one with the largest area is regular (and therefore cyclic).[7]

Self-intersecting polygons

The area of a self-intersecting polygon can be defined in two different ways, each of which gives a 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 freedom

An n-gon has 2n degrees of freedom, including 2 for position, 1 for rotational orientation, and 1 for 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 of freedom for the shape. With additional mirror-image symmetry (Dk) there are n − 1 degrees of freedom.

Product of distances from a vertex to other vertices of a regular polygon

For a regular n-gon inscribed in a unit-radius circle, the product of the distances from a given vertex to all other vertices equals n.

Generalizations of polygons

In a broad sense, a polygon is an unbounded (without ends) sequence or circuit of alternating segments (sides) and angles (corners). An ordinary polygon is unbounded because the sequence closes back in itself in a loop or circuit, while an apeirogon (infinite polygon) is unbounded because it goes on for ever so you can never reach any bounding end point. The modern mathematical 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 is another 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; this involves some "mapping" of elements from the abstract to the geometric. Such a polygon does not have to lie in a plane, or have straight sides, or enclose an area, and individual elements can

overlap 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 to explain what kind we are talking about.

A digon is a closed polygon having two sides and two corners. On the sphere, we can mark two opposing points (like the North and South poles) and join them by half a great circle. Add another arc of a different great circle and you have a digon. Tile the sphere with digons and you have a polyhedron called a hosohedron. Take just one great circle instead, run it all the way around, and add just one "corner" point, and you have a monogon or henagon – although many authorities 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 some degenerate 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 polygons

The word "polygon" comes from Late Latin polygōnum (a noun), from Greek πολύγωνον (polygōnon/polugōnon), noun use of neuter of πολύγωνος (polygōnos/polugōnos, the masculine adjective), 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 exceptions. For large numbers, mathematicians usually write the numeral itself, e.g. 17-gon. A variable can even be used, usually n-gon. This is useful if the number of sides is used in a formula.

Some special polygons also have their own names; for example the regular star pentagon is also known as the pentagram.

Polygon namesName Edges Remarks

henagon (or monogon) 1In the Euclidean plane, degenerates to a closed curve with a single vertex point on it.

digon 2In the Euclidean plane, degenerates to a closed curve with two vertex points on it.

triangle (or trigon) 3 The simplest polygon which can exist in the Euclidean plane.quadrilateral (or quadrangle or tetragon)

4 The simplest polygon which can cross itself.

pentagon 5The simplest polygon which can exist as a regular star. A star pentagon is known as a pentagram or pentacle.

hexagon 6 Avoid "sexagon" = Latin [sex-] + Greek.

heptagon 7

Avoid "septagon" = Latin [sept-] + Greek. The simplest polygon such that the regular form is not constructible with compass and straightedge. However, it can be constructed using a Neusis construction.

octagon 8

enneagon or nonagon 9"Nonagon" is commonly used but mixes Latin [novem = 9] with Greek. Some modern authors prefer "enneagon", which is pure Greek.

decagon 10

hendecagon 11Avoid "undecagon" = Latin [un-] + Greek. The simplest polygon such that the regular form cannot be constructed with compass, straightedge, and angle trisector.

dodecagon 12 Avoid "duodecagon" = Latin [duo-] + Greek.tridecagon (or triskaidecagon)

13

tetradecagon (or tetrakaidecagon)

14

pentadecagon (or quindecagon or pentakaidecagon)

15

hexadecagon (or hexakaidecagon)

16

heptadecagon (or heptakaidecagon)

17

octadecagon (or octakaidecagon)

18

enneadecagon (or enneakaidecagon or nonadecagon)

19

icosagon 20triacontagon 30

hectogon 100"hectogon" is the Greek name (see hectometer), "centagon" is a Latin-Greek hybrid; neither is widely attested.

chiliagon 1000 René Descartes,[8] Immanuel Kant,[9] David Hume, [10] and others have used the chiliagon as an example in philosophical

discussion.myriagon 10,000

megagon [11] [12] [13] 1,000,000

As with René Descartes' example of the chiliagon, the million-sided polygon has been used as an illustration of a well-defined 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 sides

Constructing higher names

To construct the name of a polygon with more than 20 and less than 100 edges, combine the prefixes as follows

Tensand Ones final suffix

-kai-

1 -hena-

-gon

20 icosa- 2 -di-30 triaconta- 3 -tri-40 tetraconta- 4 -tetra-50 pentaconta- 5 -penta-60 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 (see also examples above).

Alternatively, the system used for naming the higher alkanes (completely saturated hydrocarbons) can be used:

Ones Tens final suffix1 hen- 10 deca-

-gon

2 do- 20 -cosa-3 tri- 30 triaconta-4 tetra- 40 tetraconta-5 penta- 50 pentaconta-6 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 dotetracontagon

and a 50-sided figure

Tens and Ones final suffix full polygon namepentaconta-   -gon pentacontagon

But beyond enneagons and decagons, professional mathematicians generally prefer the aforementioned 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.

History

The component method is the concept that you can resolve vectors into two independent (therefore perpendicular) vectors (say, in the x and y directions). And, you can "put a vector back together" simply, using the distance formula and the slope of the line.

So, the component form and the direction/magnitude forms are just two different ways of specifying a vector. he Component Method for Vector Addition and Scalar Multiplication

When we mentioned in the introduction that a vector is either an ordered pair or a triplet of numbers 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 a component of the vector. Unless otherwise specified, it is normally understood that the entries correspond to the number of units the vector has in the x , y , and (for the 3D case) z directions of a plane or space. In other words, you can think of the components as simply the coordinates of the point associated with the vector. (In some sense, the vector is the point, although when we draw vectors we normally draw an arrow from the origin to the point.)

Figure %: The vector (a, b) in the Euclidean plane.

Vector Addition Using Components

Given 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 almost identical:

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-dimensional vector 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 same rules apply when we are dealing with scalar multiplication.

Scalar Multiplication of Vectors Using Components

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 scalar multiplication 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 the same dimension) by multiplying each component of the original vector by a .

Unit Vectors

For 3-dimensional vectors, it is often customary to define unit vectors pointing in the x , y , and z directions. These vectors are usually denoted by the letters i , j , and k , respectively, and all have length 1 . Thus, i = (1, 0, 0) , j = (0, 1, 0) , and k = (0, 0, 1) . This enables us to write a vector as a 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 k  

Vector Subtraction

Subtraction for vectors (as with ordinary numbers) is not a new operation. If you want to perform the vector subtraction u - v , you simply use the rules for vector addition and scalar multiplication: u - v = u + (- 1)v .

In the next section, we will see how these rules for addition and scalar multiplication of vectors can be understood in a geometric way. We will find, for instance, that vector addition can be done graphically (i.e. without even knowing the components of the vectors involved), and that scalar multiplication of a vector amounts to a change in the vector's magnitude, but does not alter its direction.

Resultant force refers to the reduction of a system of forces acting on a body to a single force and an associated torque. The choice of the point of application of the force determines the associated torque.[1] The term resultant force should be understood to refer to both the forces and torques 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 motion of the rigid body they act upon.

Associated torque

If a point R is selected as the point of application of the resultant force F of a system of n forces Fi then the associated torque T is determined from the formulas

and

It is useful to note that the point of application R of the resultant force may be anywhere along the line of action of F without changing the value of the associated torque. To see this add the vector 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 additional term including kF,

Now because F is the sum of the vectors Fi this additional term is zero, that is

and the value of the associated torque is unchanged.

Torque-free resultant

it is useful to consider whether there is a point of application R such that the associated torque is zero. This point is defined by property

where 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 the right side yield a vector that is perpendicular to F. Thus, the condition that a system of forces has a torque-free resultant can be written as

If 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 the resultant 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.

Wrench

The forces and torques acting on a rigid body can be assembled into the pair of vectors called a wrench.[2] Let P be the point of application of the force F and let R be the vector locating this point in a fixed frame. Then the pair of vectors W=(F, R×F) is called a wrench. Vectors of this form are know as screws and their mathematics formulation is called screw theory.[3][4]

The resultant force and torque on a rigid body obtained from a system of forces Fi i=1,...,n, is simply the sum of the individual wrenches Wi, that is

Notice that the case of two equal but opposite forces F and -F acting at points A and B respectively, yields the resultant W=(F-F, A×F - B× F) = (0, (A-B)×F). This shows that wrenches 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 the key branches of natural science. Read on...Natural science can be defined as a rational approach to the study of the universe and the physical world. Astronomy, biology, chemistry, earth science and physics are the main branches of 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 and galaxies and phenomena that originate outside the earth's atmosphere such as the cosmic

background radiation.

Biology or biological science is the scientific study of living things, including the study of their structure, origin, growth, evolution, function and distribution. Different branches of biology are zoology, botany, genetics, ecology, marine biology and biochemistry.

Chemistry is a branch of natural science that deals with the composition of substances as well as their properties and reactions. It involves the study of matter and its interactions with energy and itself. Today, a number of disciplines exist under the various branches of chemistry.

Earth science includes the study of the earth's system in space that includes weather and climate systems as well as the study of nonliving things such as oceans, rocks and planets. It deals with the physical aspects of the earth, such as its formation, structure, and related phenomena. It includes different branches such as geology, geography, meteorology, oceanography and astronomy.

Physics is a branch of natural science that is associated with the study of properties and interactions of time, space, energy and matter. Read more at Buzzle: http://www.buzzle.com/articles/what-are-the-main-branches-of-natural-science.html

In physics, a scalar is a simple physical quantity that is unchanged by coordinate system rotations or translations (in Newtonian mechanics), or by Lorentz transformations or central-time translations (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 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 is essentially the same as in mathematics.

An example of a scalar quantity is temperature; the temperature at a given point is a single number. Velocity, for example, is a vector quantity. Velocity in four-dimensional space is specified by three values; in a Cartesian coordinate system the values are the speeds relative to each 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 point without the distance information. Directions may be either relative to some indicated reference (the violins in a full orchestra are typically seated to the left of the conductor), or absolute according to some previously agreed upon frame of reference (New York City lies due west of Madrid). Direction is often indicated manually by an extended index finger or written as an arrow. On a vertically oriented sign representing 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 made by 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 as larger or smaller than other objects of the same kind. More formally, an object's magnitude is an ordering (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 the horizontal width of a two or three-dimensional object. In the picture to the right, the x-axis plane goes left-to-right and intersects with the y-axis and z-axis. A good example of where the x-axis is used on a computer is with the mouse. By assigning a value to the x-axis, when the mouse is moved left-to-right the x-axis value increases and decreases, which allows the computer to know where the mouse cursor is on the screen.

he vertical axis of a two-dimensional plot in Cartesian coordinates. Physicists and astronomers sometimes call this axis the ordinate, although that term is more commonly used to refer to coordinates along the -axis. n physics, a force is any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction. It is measured with the SI unit of newtons and represented by the symbol F. In other words, a force is that which can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform. Force can also be described by intuitive concepts such as a push or pull. A force has both magnitude and direction, making it a vector quantity.

The original form of Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes.[1] This law is further given to mean that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional the mass of the object. As a formula, this is 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, which decreases the velocity of an object; and torque which produces changes in rotational speed of an object. Forces which do not act uniformly on all parts of a body will also cause mechanical stresses,[2] a technical term for influences which cause deformation of matter. While mechanical stress can remain embedded in a solid object, gradually deforming it, mechanical stress in a fluid determines changes in its pressure and volume.[3][4]