Force

In physics, a force is any interaction that, when unopposed, will change the motion of an object.[1] A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.

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 with time. If the mass of the object is constant, this law implies 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 to the mass of the object.

Concepts related 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. In an extended body, each part usually applies forces on the adjacent parts; the distribution of such forces through the body is the internal mechanical stress. Such internal mechanical stresses cause no acceleration of that body as the forces balance one another. Pressure, the distribution of many small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate. Stress usually causes deformation of solid materials, or flow in fluids.

Force
Force examples
Forces can be described as a push or pull on an object. They can be due to phenomena such as gravity, magnetism, or anything that might cause a mass to accelerate.
Common symbols
F, F, F
SI unitnewton (N)
Other units
dyne, pound-force, poundal, kip, kilopond
In SI base unitskg·m/s2
Derivations from
other quantities
F = m a
Dimension

Development of the concept

Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part this was due to an incomplete understanding of the sometimes non-obvious force of friction, and a consequently inadequate view of the nature of natural motion.[2] A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved for nearly three hundred years.[3] By the early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light, and also provided insight into the forces produced by gravitation and inertia.

With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised a Standard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong, electromagnetic, weak, and gravitational.[4]:2–10[5]:79 High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction.[6]

Pre-Newtonian concepts

Aristoteles Louvre2
Aristotle famously described a force as anything that causes an object to undergo "unnatural motion"

Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids.[2]

Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotle's view, the terrestrial sphere contained four elements that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground and that they will stay that way if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force.[7] This theory, based on the everyday experience of how objects move, such as the constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of projectiles, such as the flight of arrows. The place where the archer moves the projectile was at the start of the flight, and while the projectile sailed through the air, no discernible efficient cause acts on it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path carries the projectile to its target. This explanation demands a continuum like air for change of place in general.[8]

Aristotelian physics began facing criticism in medieval science, first by John Philoponus in the 6th century.

The shortcomings of Aristotelian physics would not be fully corrected until the 17th century work of Galileo Galilei, who was influenced by the late medieval idea that objects in forced motion carried an innate force of impetus. Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove the Aristotelian theory of motion. He showed that the bodies were accelerated by gravity to an extent that was independent of their mass and argued that objects retain their velocity unless acted on by a force, for example friction.[9]

Newtonian mechanics

Sir Isaac Newton described the motion of all objects using the concepts of inertia and force, and in doing so he found they obey certain conservation laws. In 1687, Newton published his thesis Philosophiæ Naturalis Principia Mathematica.[3][10] In this work Newton set out three laws of motion that to this day are the way forces are described in physics.[10]

First law

Newton's First Law of Motion states that objects continue to move in a state of constant velocity unless acted upon by an external net force (resultant force).[10] This law is an extension of Galileo's insight that constant velocity was associated with a lack of net force (see a more detailed description of this below). Newton proposed that every object with mass has an innate inertia that functions as the fundamental equilibrium "natural state" in place of the Aristotelian idea of the "natural state of rest". That is, Newton's empirical First Law contradicts the intuitive Aristotelian belief that a net force is required to keep an object moving with constant velocity. By making rest physically indistinguishable from non-zero constant velocity, Newton's First Law directly connects inertia with the concept of relative velocities. Specifically, in systems where objects are moving with different velocities, it is impossible to determine which object is "in motion" and which object is "at rest". The laws of physics are the same in every inertial frame of reference, that is, in all frames related by a Galilean transformation.

For instance, while traveling in a moving vehicle at a constant velocity, the laws of physics do not change as a result of its motion. If a person riding within the vehicle throws a ball straight up, that person will observe it rise vertically and fall vertically and not have to apply a force in the direction the vehicle is moving. Another person, observing the moving vehicle pass by, would observe the ball follow a curving parabolic path in the same direction as the motion of the vehicle. It is the inertia of the ball associated with its constant velocity in the direction of the vehicle's motion that ensures the ball continues to move forward even as it is thrown up and falls back down. From the perspective of the person in the car, the vehicle and everything inside of it is at rest: It is the outside world that is moving with a constant speed in the opposite direction of the vehicle. Since there is no experiment that can distinguish whether it is the vehicle that is at rest or the outside world that is at rest, the two situations are considered to be physically indistinguishable. Inertia therefore applies equally well to constant velocity motion as it does to rest.

GodfreyKneller-IsaacNewton-1689
Though Sir Isaac Newton's most famous equation is
, he actually wrote down a different form for his second law of motion that did not use differential calculus.

Second law

A modern statement of Newton's Second Law is a vector equation:[Note 1]

where is the momentum of the system, and is the net (vector sum) force. If a body is in equilibrium, there is zero net force by definition (balanced forces may be present nevertheless). In contrast, the second law states that if there is an unbalanced force acting on an object it will result in the object's momentum changing over time.[10]

By the definition of momentum,

where m is the mass and is the velocity.[4]:9-1, 9-2

If Newton's second law is applied to a system of constant mass,[Note 2] m may be moved outside the derivative operator. The equation then becomes

By substituting the definition of acceleration, the algebraic version of Newton's Second Law is derived:

Newton never explicitly stated the formula in the reduced form above.[11]

Newton's Second Law asserts the direct proportionality of acceleration to force and the inverse proportionality of acceleration to mass. Accelerations can be defined through kinematic measurements. However, while kinematics are well-described through reference frame analysis in advanced physics, there are still deep questions that remain as to what is the proper definition of mass. General relativity offers an equivalence between space-time and mass, but lacking a coherent theory of quantum gravity, it is unclear as to how or whether this connection is relevant on microscales. With some justification, Newton's second law can be taken as a quantitative definition of mass by writing the law as an equality; the relative units of force and mass then are fixed.

The use of Newton's Second Law as a definition of force has been disparaged in some of the more rigorous textbooks,[4]:12-1[5]:59[12] because it is essentially a mathematical truism. Notable physicists, philosophers and mathematicians who have sought a more explicit definition of the concept of force include Ernst Mach and Walter Noll.[13][14]

Newton's Second Law can be used to measure the strength of forces. For instance, knowledge of the masses of planets along with the accelerations of their orbits allows scientists to calculate the gravitational forces on planets.

Third law

Whenever one body exerts a force on another, the latter simultaneously exerts an equal and opposite force on the first. In vector form, if is the force of body 1 on body 2 and that of body 2 on body 1, then

This law is sometimes referred to as the action-reaction law, with called the action and the reaction.

Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are interactions between different bodies,[15][Note 3] and thus that there is no such thing as a unidirectional force or a force that acts on only one body.

In a system composed of object 1 and object 2, the net force on the system due to their mutual interactions is zero:

More generally, in a closed system of particles, all internal forces are balanced. The particles may accelerate with respect to each other but the center of mass of the system will not accelerate. If an external force acts on the system, it will make the center of mass accelerate in proportion to the magnitude of the external force divided by the mass of the system.[4]:19-1[5]

Combining Newton's Second and Third Laws, it is possible to show that the linear momentum of a system is conserved.[16] In a system of two particles, if is the momentum of object 1 and the momentum of object 2, then

Using similar arguments, this can be generalized to a system with an arbitrary number of particles. In general, as long as all forces are due to the interaction of objects with mass, it is possible to define a system such that net momentum is never lost nor gained.[4][5]

Special theory of relativity

In the special theory of relativity, mass and energy are equivalent (as can be seen by calculating the work required to accelerate an object). When an object's velocity increases, so does its energy and hence its mass equivalent (inertia). It thus requires more force to accelerate it the same amount than it did at a lower velocity. Newton's Second Law

remains valid because it is a mathematical definition.[17]:855–876 But for relativistic momentum to be conserved, it must be redefined as:

where is the rest mass and the speed of light.

The relativistic expression relating force and acceleration for a particle with constant non-zero rest mass moving in the direction is:

where

is called the Lorentz factor.[18]

In the early history of relativity, the expressions and were called longitudinal and transverse mass. Relativistic force does not produce a constant acceleration, but an ever-decreasing acceleration as the object approaches the speed of light. Note that approaches asymptotically an infinite value and is undefined for an object with a non-zero rest mass as it approaches the speed of light, and the theory yields no prediction at that speed.

If is very small compared to , then is very close to 1 and

is a close approximation. Even for use in relativity, however, one can restore the form of

through the use of four-vectors. This relation is correct in relativity when is the four-force, is the invariant mass, and is the four-acceleration.[19]

Descriptions

Freebodydiagram3 pn
Free body diagrams of a block on a flat surface and an inclined plane. Forces are resolved and added together to determine their magnitudes and the net force.

Since forces are perceived as pushes or pulls, this can provide an intuitive understanding for describing forces.[3] As with other physical concepts (e.g. temperature), the intuitive understanding of forces is quantified using precise operational definitions that are consistent with direct observations and compared to a standard measurement scale. Through experimentation, it is determined that laboratory measurements of forces are fully consistent with the conceptual definition of force offered by Newtonian mechanics.

Forces act in a particular direction and have sizes dependent upon how strong the push or pull is. Because of these characteristics, forces are classified as "vector quantities". This means that forces follow a different set of mathematical rules than physical quantities that do not have direction (denoted scalar quantities). For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result. If both of these pieces of information are not known for each force, the situation is ambiguous. For example, if you know that two people are pulling on the same rope with known magnitudes of force but you do not know which direction either person is pulling, it is impossible to determine what the acceleration of the rope will be. The two people could be pulling against each other as in tug of war or the two people could be pulling in the same direction. In this simple one-dimensional example, without knowing the direction of the forces it is impossible to decide whether the net force is the result of adding the two force magnitudes or subtracting one from the other. Associating forces with vectors avoids such problems.

Historically, forces were first quantitatively investigated in conditions of static equilibrium where several forces canceled each other out. Such experiments demonstrate the crucial properties that forces are additive vector quantities: they have magnitude and direction.[3] When two forces act on a point particle, the resulting force, the resultant (also called the net force), can be determined by following the parallelogram rule of vector addition: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that is equal in magnitude and direction to the transversal of the parallelogram.[4][5] The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action. However, if the forces are acting on an extended body, their respective lines of application must also be specified in order to account for their effects on the motion of the body.

Free-body diagrams can be used as a convenient way to keep track of forces acting on a system. Ideally, these diagrams are drawn with the angles and relative magnitudes of the force vectors preserved so that graphical vector addition can be done to determine the net force.[20]

As well as being added, forces can also be resolved into independent components at right angles to each other. A horizontal force pointing northeast can therefore be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions.[21] This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on the magnitude or direction of the other. Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right-angles to the other two.[4][5]

Equilibrium

Equilibrium occurs when the resultant force acting on a point particle is zero (that is, the vector sum of all forces is zero). When dealing with an extended body, it is also necessary that the net torque be zero.

There are two kinds of equilibrium: static equilibrium and dynamic equilibrium.

Static

Static equilibrium was understood well before the invention of classical mechanics. Objects that are at rest have zero net force acting on them.[22]

The simplest case of static equilibrium occurs when two forces are equal in magnitude but opposite in direction. For example, an object on a level surface is pulled (attracted) downward toward the center of the Earth by the force of gravity. At the same time, a force is applied by the surface that resists the downward force with equal upward force (called a normal force). The situation produces zero net force and hence no acceleration.[3]

Pushing against an object that rests on a frictional surface can result in a situation where the object does not move because the applied force is opposed by static friction, generated between the object and the table surface. For a situation with no movement, the static friction force exactly balances the applied force resulting in no acceleration. The static friction increases or decreases in response to the applied force up to an upper limit determined by the characteristics of the contact between the surface and the object.[3]

A static equilibrium between two forces is the most usual way of measuring forces, using simple devices such as weighing scales and spring balances. For example, an object suspended on a vertical spring scale experiences the force of gravity acting on the object balanced by a force applied by the "spring reaction force", which equals the object's weight. Using such tools, some quantitative force laws were discovered: that the force of gravity is proportional to volume for objects of constant density (widely exploited for millennia to define standard weights); Archimedes' principle for buoyancy; Archimedes' analysis of the lever; Boyle's law for gas pressure; and Hooke's law for springs. These were all formulated and experimentally verified before Isaac Newton expounded his Three Laws of Motion.[3][4][5]

Dynamic

Galileo.arp.300pix
Galileo Galilei was the first to point out the inherent contradictions contained in Aristotle's description of forces.

Dynamic equilibrium was first described by Galileo who noticed that certain assumptions of Aristotelian physics were contradicted by observations and logic. Galileo realized that simple velocity addition demands that the concept of an "absolute rest frame" did not exist. Galileo concluded that motion in a constant velocity was completely equivalent to rest. This was contrary to Aristotle's notion of a "natural state" of rest that objects with mass naturally approached. Simple experiments showed that Galileo's understanding of the equivalence of constant velocity and rest were correct. For example, if a mariner dropped a cannonball from the crow's nest of a ship moving at a constant velocity, Aristotelian physics would have the cannonball fall straight down while the ship moved beneath it. Thus, in an Aristotelian universe, the falling cannonball would land behind the foot of the mast of a moving ship. However, when this experiment is actually conducted, the cannonball always falls at the foot of the mast, as if the cannonball knows to travel with the ship despite being separated from it. Since there is no forward horizontal force being applied on the cannonball as it falls, the only conclusion left is that the cannonball continues to move with the same velocity as the boat as it falls. Thus, no force is required to keep the cannonball moving at the constant forward velocity.[9]

Moreover, any object traveling at a constant velocity must be subject to zero net force (resultant force). This is the definition of dynamic equilibrium: when all the forces on an object balance but it still moves at a constant velocity.

A simple case of dynamic equilibrium occurs in constant velocity motion across a surface with kinetic friction. In such a situation, a force is applied in the direction of motion while the kinetic friction force exactly opposes the applied force. This results in zero net force, but since the object started with a non-zero velocity, it continues to move with a non-zero velocity. Aristotle misinterpreted this motion as being caused by the applied force. However, when kinetic friction is taken into consideration it is clear that there is no net force causing constant velocity motion.[4][5]

Forces in quantum mechanics

The notion "force" keeps its meaning in quantum mechanics, though one is now dealing with operators instead of classical variables and though the physics is now described by the Schrödinger equation instead of Newtonian equations. This has the consequence that the results of a measurement are now sometimes "quantized", i.e. they appear in discrete portions. This is, of course, difficult to imagine in the context of "forces". However, the potentials V(x,y,z) or fields, from which the forces generally can be derived, are treated similarly to classical position variables, i.e., .

This becomes different only in the framework of quantum field theory, where these fields are also quantized.

However, already in quantum mechanics there is one "caveat", namely the particles acting onto each other do not only possess the spatial variable, but also a discrete intrinsic angular momentum-like variable called the "spin", and there is the Pauli exclusion principle relating the space and the spin variables. Depending on the value of the spin, identical particles split into two different classes, fermions and bosons. If two identical fermions (e.g. electrons) have a symmetric spin function (e.g. parallel spins) the spatial variables must be antisymmetric (i.e. they exclude each other from their places much as if there was a repulsive force), and vice versa, i.e. for antiparallel spins the position variables must be symmetric (i.e. the apparent force must be attractive). Thus in the case of two fermions there is a strictly negative correlation between spatial and spin variables, whereas for two bosons (e.g. quanta of electromagnetic waves, photons) the correlation is strictly positive.

Thus the notion "force" loses already part of its meaning.

Feynman diagrams

Beta Negative Decay
Feynman diagram for the decay of a neutron into a proton. The W boson is between two vertices indicating a repulsion.

In modern particle physics, forces and the acceleration of particles are explained as a mathematical by-product of exchange of momentum-carrying gauge bosons. With the development of quantum field theory and general relativity, it was realized that force is a redundant concept arising from conservation of momentum (4-momentum in relativity and momentum of virtual particles in quantum electrodynamics). The conservation of momentum can be directly derived from the homogeneity or symmetry of space and so is usually considered more fundamental than the concept of a force. Thus the currently known fundamental forces are considered more accurately to be "fundamental interactions".[6]:199–128 When particle A emits (creates) or absorbs (annihilates) virtual particle B, a momentum conservation results in recoil of particle A making impression of repulsion or attraction between particles A A' exchanging by B. This description applies to all forces arising from fundamental interactions. While sophisticated mathematical descriptions are needed to predict, in full detail, the accurate result of such interactions, there is a conceptually simple way to describe such interactions through the use of Feynman diagrams. In a Feynman diagram, each matter particle is represented as a straight line (see world line) traveling through time, which normally increases up or to the right in the diagram. Matter and anti-matter particles are identical except for their direction of propagation through the Feynman diagram. World lines of particles intersect at interaction vertices, and the Feynman diagram represents any force arising from an interaction as occurring at the vertex with an associated instantaneous change in the direction of the particle world lines. Gauge bosons are emitted away from the vertex as wavy lines and, in the case of virtual particle exchange, are absorbed at an adjacent vertex.[23]

The utility of Feynman diagrams is that other types of physical phenomena that are part of the general picture of fundamental interactions but are conceptually separate from forces can also be described using the same rules. For example, a Feynman diagram can describe in succinct detail how a neutron decays into an electron, proton, and neutrino, an interaction mediated by the same gauge boson that is responsible for the weak nuclear force.[23]

Fundamental forces

All of the known forces of the universe are classified into four fundamental interactions. The strong and the weak forces are nuclear forces that act only at very short distances, and are responsible for the interactions between subatomic particles, including nucleons and compound nuclei. The electromagnetic force acts between electric charges, and the gravitational force acts between masses. All other forces in nature derive from these four fundamental interactions. For example, friction is a manifestation of the electromagnetic force acting between atoms of two surfaces, and the Pauli exclusion principle,[24] which does not permit atoms to pass through each other. Similarly, the forces in springs, modeled by Hooke's law, are the result of electromagnetic forces and the Pauli exclusion principle acting together to return an object to its equilibrium position. Centrifugal forces are acceleration forces that arise simply from the acceleration of rotating frames of reference.[4]:12-11[5]:359

The fundamental theories for forces developed from the unification of different ideas. For example, Sir. Isaac Newton unified, with his universal theory of gravitation, the force responsible for objects falling near the surface of the Earth with the force responsible for the falling of celestial bodies about the Earth (the Moon) and around the Sun (the planets). Michael Faraday and James Clerk Maxwell demonstrated that electric and magnetic forces were unified through a theory of electromagnetism. In the 20th century, the development of quantum mechanics led to a modern understanding that the first three fundamental forces (all except gravity) are manifestations of matter (fermions) interacting by exchanging virtual particles called gauge bosons.[25] This standard model of particle physics assumes a similarity between the forces and led scientists to predict the unification of the weak and electromagnetic forces in electroweak theory, which was subsequently confirmed by observation. The complete formulation of the standard model predicts an as yet unobserved Higgs mechanism, but observations such as neutrino oscillations suggest that the standard model is incomplete. A Grand Unified Theory that allows for the combination of the electroweak interaction with the strong force is held out as a possibility with candidate theories such as supersymmetry proposed to accommodate some of the outstanding unsolved problems in physics. Physicists are still attempting to develop self-consistent unification models that would combine all four fundamental interactions into a theory of everything. Einstein tried and failed at this endeavor, but currently the most popular approach to answering this question is string theory.[6]:212–219

The four fundamental forces of nature[26]
Property/Interaction Gravitation Weak Electromagnetic Strong
(Electroweak) Fundamental Residual
Acts on: Mass - Energy Flavor Electric charge Color charge Atomic nuclei
Particles experiencing: All Quarks, leptons Electrically charged Quarks, Gluons Hadrons
Particles mediating: Graviton
(not yet observed)
W+ W Z0 γ Gluons Mesons
Strength in the scale of quarks: 10−41 10−4 1 60 Not applicable
to quarks
Strength in the scale of
protons/neutrons:
10−36 10−7 1 Not applicable
to hadrons
20

Gravitational

Falling ball
Images of a freely falling basketball taken with a stroboscope at 20 flashes per second. The distance units on the right are multiples of about 12 millimeters. The basketball starts at rest. At the time of the first flash (distance zero) it is released, after which the number of units fallen is equal to the square of the number of flashes.

What we now call gravity was not identified as a universal force until the work of Isaac Newton. Before Newton, the tendency for objects to fall towards the Earth was not understood to be related to the motions of celestial objects. Galileo was instrumental in describing the characteristics of falling objects by determining that the acceleration of every object in free-fall was constant and independent of the mass of the object. Today, this acceleration due to gravity towards the surface of the Earth is usually designated as and has a magnitude of about 9.81 meters per second squared (this measurement is taken from sea level and may vary depending on location), and points toward the center of the Earth.[27] This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass. Thus an object that has a mass of will experience a force:

For an object in free-fall, this force is unopposed and the net force on the object is its weight. For objects not in free-fall, the force of gravity is opposed by the reaction forces applied by their supports. For example, a person standing on the ground experiences zero net force, since a normal force (a reaction force) is exerted by the ground upward on the person that counterbalances his weight that is directed downward.[4][5]

Newton's contribution to gravitational theory was to unify the motions of heavenly bodies, which Aristotle had assumed were in a natural state of constant motion, with falling motion observed on the Earth. He proposed a law of gravity that could account for the celestial motions that had been described earlier using Kepler's laws of planetary motion.[28]

Newton came to realize that the effects of gravity might be observed in different ways at larger distances. In particular, Newton determined that the acceleration of the Moon around the Earth could be ascribed to the same force of gravity if the acceleration due to gravity decreased as an inverse square law. Further, Newton realized that the acceleration of a body due to gravity is proportional to the mass of the other attracting body.[28] Combining these ideas gives a formula that relates the mass () and the radius () of the Earth to the gravitational acceleration:

where the vector direction is given by , is the unit vector directed outward from the center of the Earth.[10]

In this equation, a dimensional constant is used to describe the relative strength of gravity. This constant has come to be known as Newton's Universal Gravitation Constant,[29] though its value was unknown in Newton's lifetime. Not until 1798 was Henry Cavendish able to make the first measurement of using a torsion balance; this was widely reported in the press as a measurement of the mass of the Earth since knowing could allow one to solve for the Earth's mass given the above equation. Newton, however, realized that since all celestial bodies followed the same laws of motion, his law of gravity had to be universal. Succinctly stated, Newton's Law of Gravitation states that the force on a spherical object of mass due to the gravitational pull of mass is

where is the distance between the two objects' centers of mass and is the unit vector pointed in the direction away from the center of the first object toward the center of the second object.[10]

This formula was powerful enough to stand as the basis for all subsequent descriptions of motion within the solar system until the 20th century. During that time, sophisticated methods of perturbation analysis[30] were invented to calculate the deviations of orbits due to the influence of multiple bodies on a planet, moon, comet, or asteroid. The formalism was exact enough to allow mathematicians to predict the existence of the planet Neptune before it was observed.[31]

GRAVITY A powerful new probe of black holes
Instruments like GRAVITY provide a powerful probe for gravity force detection.[32]

Mercury's orbit, however, did not match that predicted by Newton's Law of Gravitation. Some astrophysicists predicted the existence of another planet (Vulcan) that would explain the discrepancies; however no such planet could be found. When Albert Einstein formulated his theory of general relativity (GR) he turned his attention to the problem of Mercury's orbit and found that his theory added a correction, which could account for the discrepancy. This was the first time that Newton's Theory of Gravity had been shown to be inexact.[33]

Since then, general relativity has been acknowledged as the theory that best explains gravity. In GR, gravitation is not viewed as a force, but rather, objects moving freely in gravitational fields travel under their own inertia in straight lines through curved space-time – defined as the shortest space-time path between two space-time events. From the perspective of the object, all motion occurs as if there were no gravitation whatsoever. It is only when observing the motion in a global sense that the curvature of space-time can be observed and the force is inferred from the object's curved path. Thus, the straight line path in space-time is seen as a curved line in space, and it is called the ballistic trajectory of the object. For example, a basketball thrown from the ground moves in a parabola, as it is in a uniform gravitational field. Its space-time trajectory is almost a straight line, slightly curved (with the radius of curvature of the order of few light-years). The time derivative of the changing momentum of the object is what we label as "gravitational force".[5]

Electromagnetic

The electrostatic force was first described in 1784 by Coulomb as a force that existed intrinsically between two charges.[17]:519 The properties of the electrostatic force were that it varied as an inverse square law directed in the radial direction, was both attractive and repulsive (there was intrinsic polarity), was independent of the mass of the charged objects, and followed the superposition principle. Coulomb's law unifies all these observations into one succinct statement.[34]

Subsequent mathematicians and physicists found the construct of the electric field to be useful for determining the electrostatic force on an electric charge at any point in space. The electric field was based on using a hypothetical "test charge" anywhere in space and then using Coulomb's Law to determine the electrostatic force.[35]:4-6 to 4-8 Thus the electric field anywhere in space is defined as

where is the magnitude of the hypothetical test charge.

Meanwhile, the Lorentz force of magnetism was discovered to exist between two electric currents. It has the same mathematical character as Coulomb's Law with the proviso that like currents attract and unlike currents repel. Similar to the electric field, the magnetic field can be used to determine the magnetic force on an electric current at any point in space. In this case, the magnitude of the magnetic field was determined to be

where is the magnitude of the hypothetical test current and is the length of hypothetical wire through which the test current flows. The magnetic field exerts a force on all magnets including, for example, those used in compasses. The fact that the Earth's magnetic field is aligned closely with the orientation of the Earth's axis causes compass magnets to become oriented because of the magnetic force pulling on the needle.

Through combining the definition of electric current as the time rate of change of electric charge, a rule of vector multiplication called Lorentz's Law describes the force on a charge moving in a magnetic field.[35] The connection between electricity and magnetism allows for the description of a unified electromagnetic force that acts on a charge. This force can be written as a sum of the electrostatic force (due to the electric field) and the magnetic force (due to the magnetic field). Fully stated, this is the law:

where is the electromagnetic force, is the magnitude of the charge of the particle, is the electric field, is the velocity of the particle that is crossed with the magnetic field ().

The origin of electric and magnetic fields would not be fully explained until 1864 when James Clerk Maxwell unified a number of earlier theories into a set of 20 scalar equations, which were later reformulated into 4 vector equations by Oliver Heaviside and Josiah Willard Gibbs.[36] These "Maxwell Equations" fully described the sources of the fields as being stationary and moving charges, and the interactions of the fields themselves. This led Maxwell to discover that electric and magnetic fields could be "self-generating" through a wave that traveled at a speed that he calculated to be the speed of light. This insight united the nascent fields of electromagnetic theory with optics and led directly to a complete description of the electromagnetic spectrum.[37]

However, attempting to reconcile electromagnetic theory with two observations, the photoelectric effect, and the nonexistence of the ultraviolet catastrophe, proved troublesome. Through the work of leading theoretical physicists, a new theory of electromagnetism was developed using quantum mechanics. This final modification to electromagnetic theory ultimately led to quantum electrodynamics (or QED), which fully describes all electromagnetic phenomena as being mediated by wave–particles known as photons. In QED, photons are the fundamental exchange particle, which described all interactions relating to electromagnetism including the electromagnetic force.[Note 4]

Strong nuclear

There are two "nuclear forces", which today are usually described as interactions that take place in quantum theories of particle physics. The strong nuclear force[17]:940 is the force responsible for the structural integrity of atomic nuclei while the weak nuclear force[17]:951 is responsible for the decay of certain nucleons into leptons and other types of hadrons.[4][5]

The strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD).[38] The strong force is the fundamental force mediated by gluons, acting upon quarks, antiquarks, and the gluons themselves. The (aptly named) strong interaction is the "strongest" of the four fundamental forces.

The strong force only acts directly upon elementary particles. However, a residual of the force is observed between hadrons (the best known example being the force that acts between nucleons in atomic nuclei) as the nuclear force. Here the strong force acts indirectly, transmitted as gluons, which form part of the virtual pi and rho mesons, which classically transmit the nuclear force (see this topic for more). The failure of many searches for free quarks has shown that the elementary particles affected are not directly observable. This phenomenon is called color confinement.

Weak nuclear

The weak force is due to the exchange of the heavy W and Z bosons. Its most familiar effect is beta decay (of neutrons in atomic nuclei) and the associated radioactivity. The word "weak" derives from the fact that the field strength is some 1013 times less than that of the strong force. Still, it is stronger than gravity over short distances. A consistent electroweak theory has also been developed, which shows that electromagnetic forces and the weak force are indistinguishable at a temperatures in excess of approximately 1015 kelvins. Such temperatures have been probed in modern particle accelerators and show the conditions of the universe in the early moments of the Big Bang.

Non-fundamental forces

Some forces are consequences of the fundamental ones. In such situations, idealized models can be utilized to gain physical insight.

Normal force

Incline
FN represents the normal force exerted on the object.

The normal force is due to repulsive forces of interaction between atoms at close contact. When their electron clouds overlap, Pauli repulsion (due to fermionic nature of electrons) follows resulting in the force that acts in a direction normal to the surface interface between two objects.[17]:93 The normal force, for example, is responsible for the structural integrity of tables and floors as well as being the force that responds whenever an external force pushes on a solid object. An example of the normal force in action is the impact force on an object crashing into an immobile surface.[4][5]

Friction

Friction is a surface force that opposes relative motion. The frictional force is directly related to the normal force that acts to keep two solid objects separated at the point of contact. There are two broad classifications of frictional forces: static friction and kinetic friction.

The static friction force () will exactly oppose forces applied to an object parallel to a surface contact up to the limit specified by the coefficient of static friction () multiplied by the normal force (). In other words, the magnitude of the static friction force satisfies the inequality:

The kinetic friction force () is independent of both the forces applied and the movement of the object. Thus, the magnitude of the force equals:

where is the coefficient of kinetic friction. For most surface interfaces, the coefficient of kinetic friction is less than the coefficient of static friction.

Tension

Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and unstretchable. They can be combined with ideal pulleys, which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action-reaction pairs so that if two objects are connected by an ideal string, any force directed along the string by the first object is accompanied by a force directed along the string in the opposite direction by the second object.[39] By connecting the same string multiple times to the same object through the use of a set-up that uses movable pulleys, the tension force on a load can be multiplied. For every string that acts on a load, another factor of the tension force in the string acts on the load. However, even though such machines allow for an increase in force, there is a corresponding increase in the length of string that must be displaced in order to move the load. These tandem effects result ultimately in the conservation of mechanical energy since the work done on the load is the same no matter how complicated the machine.[4][5][40]

Elastic force

Mass-spring-system
Fk is the force that responds to the load on the spring

An elastic force acts to return a spring to its natural length. An ideal spring is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring from its equilibrium position.[41] This linear relationship was described by Robert Hooke in 1676, for whom Hooke's law is named. If is the displacement, the force exerted by an ideal spring equals:

where is the spring constant (or force constant), which is particular to the spring. The minus sign accounts for the tendency of the force to act in opposition to the applied load.[4][5]

Continuum mechanics

Stokes sphere
When the drag force () associated with air resistance becomes equal in magnitude to the force of gravity on a falling object (), the object reaches a state of dynamic equilibrium at terminal velocity.

Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. However, in real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together the atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids, differences in pressure result in forces being directed along the pressure gradients as follows:

where is the volume of the object in the fluid and is the scalar function that describes the pressure at all locations in space. Pressure gradients and differentials result in the buoyant force for fluids suspended in gravitational fields, winds in atmospheric science, and the lift associated with aerodynamics and flight.[4][5]

A specific instance of such a force that is associated with dynamic pressure is fluid resistance: a body force that resists the motion of an object through a fluid due to viscosity. For so-called "Stokes' drag" the force is approximately proportional to the velocity, but opposite in direction:

where:

is a constant that depends on the properties of the fluid and the dimensions of the object (usually the cross-sectional area), and
is the velocity of the object.[4][5]

More formally, forces in continuum mechanics are fully described by a stresstensor with terms that are roughly defined as

where is the relevant cross-sectional area for the volume for which the stress-tensor is being calculated. This formalism includes pressure terms associated with forces that act normal to the cross-sectional area (the matrix diagonals of the tensor) as well as shear terms associated with forces that act parallel to the cross-sectional area (the off-diagonal elements). The stress tensor accounts for forces that cause all strains (deformations) including also tensile stresses and compressions.[3][5]:133–134[35]:38-1–38-11

Fictitious forces

There are forces that are frame dependent, meaning that they appear due to the adoption of non-Newtonian (that is, non-inertial) reference frames. Such forces include the centrifugal force and the Coriolis force.[42] These forces are considered fictitious because they do not exist in frames of reference that are not accelerating.[4][5] Because these forces are not genuine they are also referred to as "pseudo forces".[4]:12-11

In general relativity, gravity becomes a fictitious force that arises in situations where spacetime deviates from a flat geometry. As an extension, Kaluza–Klein theory and string theory ascribe electromagnetism and the other fundamental forces respectively to the curvature of differently scaled dimensions, which would ultimately imply that all forces are fictitious.

Rotations and torque

Torque animation
Relationship between force (F), torque (τ), and momentum vectors (p and L) in a rotating system.

Forces that cause extended objects to rotate are associated with torques. Mathematically, the torque of a force is defined relative to an arbitrary reference point as the cross-product:

where

is the position vector of the force application point relative to the reference point.

Torque is the rotation equivalent of force in the same way that angle is the rotational equivalent for position, angular velocity for velocity, and angular momentum for momentum. As a consequence of Newton's First Law of Motion, there exists rotational inertia that ensures that all bodies maintain their angular momentum unless acted upon by an unbalanced torque. Likewise, Newton's Second Law of Motion can be used to derive an analogous equation for the instantaneous angular acceleration of the rigid body:

where

is the moment of inertia of the body
is the angular acceleration of the body.

This provides a definition for the moment of inertia, which is the rotational equivalent for mass. In more advanced treatments of mechanics, where the rotation over a time interval is described, the moment of inertia must be substituted by the tensor that, when properly analyzed, fully determines the characteristics of rotations including precession and nutation.

Equivalently, the differential form of Newton's Second Law provides an alternative definition of torque:

[43] where is the angular momentum of the particle.

Newton's Third Law of Motion requires that all objects exerting torques themselves experience equal and opposite torques,[44] and therefore also directly implies the conservation of angular momentum for closed systems that experience rotations and revolutions through the action of internal torques.

Centripetal force

For an object accelerating in circular motion, the unbalanced force acting on the object equals:[45]

where is the mass of the object, is the velocity of the object and is the distance to the center of the circular path and is the unit vector pointing in the radial direction outwards from the center. This means that the unbalanced centripetal force felt by any object is always directed toward the center of the curving path. Such forces act perpendicular to the velocity vector associated with the motion of an object, and therefore do not change the speed of the object (magnitude of the velocity), but only the direction of the velocity vector. The unbalanced force that accelerates an object can be resolved into a component that is perpendicular to the path, and one that is tangential to the path. This yields both the tangential force, which accelerates the object by either slowing it down or speeding it up, and the radial (centripetal) force, which changes its direction.[4][5]

Kinematic integrals

Forces can be used to define a number of physical concepts by integrating with respect to kinematic variables. For example, integrating with respect to time gives the definition of impulse:[46]

which by Newton's Second Law must be equivalent to the change in momentum (yielding the Impulse momentum theorem).

Similarly, integrating with respect to position gives a definition for the work done by a force:[4]:13-3

which is equivalent to changes in kinetic energy (yielding the work energy theorem).[4]:13-3

Power P is the rate of change dW/dt of the work W, as the trajectory is extended by a position change in a time interval dt:[4]:13-2

with the velocity.

Potential energy

Instead of a force, often the mathematically related concept of a potential energy field can be used for convenience. For instance, the gravitational force acting upon an object can be seen as the action of the gravitational field that is present at the object's location. Restating mathematically the definition of energy (via the definition of work), a potential scalar field is defined as that field whose gradient is equal and opposite to the force produced at every point:

Forces can be classified as conservative or nonconservative. Conservative forces are equivalent to the gradient of a potential while nonconservative forces are not.[4][5]

Conservative forces

A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms. This means that for a closed system, the net mechanical energy is conserved whenever a conservative force acts on the system. The force, therefore, is related directly to the difference in potential energy between two different locations in space,[47] and can be considered to be an artifact of the potential field in the same way that the direction and amount of a flow of water can be considered to be an artifact of the contour map of the elevation of an area.[4][5]

Conservative forces include gravity, the electromagnetic force, and the spring force. Each of these forces has models that are dependent on a position often given as a radial vector emanating from spherically symmetric potentials.[48] Examples of this follow:

For gravity:

where is the gravitational constant, and is the mass of object n.

For electrostatic forces:

where is electric permittivity of free space, and is the electric charge of object n.

For spring forces:

where is the spring constant.[4][5]

Nonconservative forces

For certain physical scenarios, it is impossible to model forces as being due to gradient of potentials. This is often due to macrophysical considerations that yield forces as arising from a macroscopic statistical average of microstates. For example, friction is caused by the gradients of numerous electrostatic potentials between the atoms, but manifests as a force model that is independent of any macroscale position vector. Nonconservative forces other than friction include other contact forces, tension, compression, and drag. However, for any sufficiently detailed description, all these forces are the results of conservative ones since each of these macroscopic forces are the net results of the gradients of microscopic potentials.[4][5]

The connection between macroscopic nonconservative forces and microscopic conservative forces is described by detailed treatment with statistical mechanics. In macroscopic closed systems, nonconservative forces act to change the internal energies of the system, and are often associated with the transfer of heat. According to the Second law of thermodynamics, nonconservative forces necessarily result in energy transformations within closed systems from ordered to more random conditions as entropy increases.[4][5]

Units of measurement

The SI unit of force is the newton (symbol N), which is the force required to accelerate a one kilogram mass at a rate of one meter per second squared, or kg·m·s−2.[49] The corresponding CGS unit is the dyne, the force required to accelerate a one gram mass by one centimeter per second squared, or g·cm·s−2. A newton is thus equal to 100,000 dynes.

The gravitational foot-pound-second English unit of force is the pound-force (lbf), defined as the force exerted by gravity on a pound-mass in the standard gravitational field of 9.80665 m·s−2.[49] The pound-force provides an alternative unit of mass: one slug is the mass that will accelerate by one foot per second squared when acted on by one pound-force.[49]

An alternative unit of force in a different foot-pound-second system, the absolute fps system, is the poundal, defined as the force required to accelerate a one-pound mass at a rate of one foot per second squared.[49] The units of slug and poundal are designed to avoid a constant of proportionality in Newton's Second Law.

The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass.[49] The kilogram-force leads to an alternate, but rarely used unit of mass: the metric slug (sometimes mug or hyl) is that mass that accelerates at 1 m·s−2 when subjected to a force of 1 kgf. The kilogram-force is not a part of the modern SI system, and is generally deprecated; however it still sees use for some purposes as expressing aircraft weight, jet thrust, bicycle spoke tension, torque wrench settings and engine output torque. Other arcane units of force include the sthène, which is equivalent to 1000 N, and the kip, which is equivalent to 1000 lbf.

Units of force
newton
(SI unit)
dyne kilogram-force,
kilopond
pound-force poundal
1 N ≡ 1 kg⋅m/s2 = 105 dyn ≈ 0.10197 kp ≈ 0.22481 lbf ≈ 7.2330 pdl
1 dyn = 10−5 N ≡ 1 g⋅cm/s2 ≈ 1.0197 × 10−6 kp ≈ 2.2481 × 10−6 lbf ≈ 7.2330 × 10−5 pdl
1 kp = 9.80665 N = 980665 dyn gn ⋅ (1 kg) ≈ 2.2046 lbf ≈ 70.932 pdl
1 lbf ≈ 4.448222 N ≈ 444822 dyn ≈ 0.45359 kp gn ⋅ (1 lb) ≈ 32.174 pdl
1 pdl ≈ 0.138255 N ≈ 13825 dyn ≈ 0.014098 kp ≈ 0.031081 lbf ≡ 1 lb⋅ft/s2
The value of gn as used in the official definition of the kilogram-force is used here for all gravitational units.

See also Ton-force.

Force measurement

See force gauge, spring scale, load cell

See also

Notes

  1. ^ Newton's Principia Mathematica actually used a finite difference version of this equation based upon impulse. See Impulse.
  2. ^ "It is important to note that we cannot derive a general expression for Newton's second law for variable mass systems by treating the mass in F = dP/dt = d(Mv) as a variable. [...] We can use F = dP/dt to analyze variable mass systems only if we apply it to an entire system of constant mass having parts among which there is an interchange of mass." [Emphasis as in the original] (Halliday, Resnick & Krane 2001, p. 199)
  3. ^ "Any single force is only one aspect of a mutual interaction between two bodies." (Halliday, Resnick & Krane 2001, pp. 78–79)
  4. ^ For a complete library on quantum mechanics see Quantum mechanics – References

References

  1. ^ Nave, C.R. (2014). "Force". Hyperphysics. Dept. of Physics and Astronomy, Georgia State University. Retrieved 15 August 2014.
  2. ^ a b Heath, T.L. (1897). The Works of Archimedes (1897). The unabridged work in PDF form (19 MB). Internet Archive. Retrieved 2007-10-14.
  3. ^ a b c d e f g h University Physics, Sears, Young & Zemansky, pp. 18–38
  4. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab Feynman volume 1
  5. ^ a b c d e f g h i j k l m n o p q r s t u v w x y Kleppner & Kolenkow 2010
  6. ^ a b c Weinberg, S. (1994). Dreams of a Final Theory. Vintage Books. ISBN 978-0-679-74408-5.
  7. ^ Lang, Helen S. (1998). The order of nature in Aristotle's physics : place and the elements (1. publ. ed.). Cambridge: Cambridge Univ. Press. ISBN 9780521624534.
  8. ^ Hetherington, Norriss S. (1993). Cosmology: Historical, Literary, Philosophical, Religious, and Scientific Perspectives. Garland Reference Library of the Humanities. p. 100. ISBN 978-0-8153-1085-3.
  9. ^ a b Drake, Stillman (1978). Galileo At Work. Chicago: University of Chicago Press. ISBN 0-226-16226-5
  10. ^ a b c d e f Newton, Isaac (1999). The Principia Mathematical Principles of Natural Philosophy. Berkeley: University of California Press. ISBN 978-0-520-08817-7. This is a recent translation into English by I. Bernard Cohen and Anne Whitman, with help from Julia Budenz.
  11. ^ Howland, R.A. (2006). Intermediate dynamics a linear algebraic approach (Online-Ausg. ed.). New York: Springer. pp. 255–256. ISBN 9780387280592.
  12. ^ One exception to this rule is: Landau, L.D.; Akhiezer, A.I.; Lifshitz, A.M. (196). General Physics; mechanics and molecular physics (First English ed.). Oxford: Pergamon Press. ISBN 978-0-08-003304-4. Translated by: J.B. Sykes, A.D. Petford, and C.L. Petford. LCCN 67--30260. In section 7, pp. 12–14, this book defines force as dp/dt.
  13. ^ Jammer, Max (1999). Concepts of force : a study in the foundations of dynamics (Facsim. ed.). Mineola, N.Y.: Dover Publications. pp. 220–222. ISBN 9780486406893.
  14. ^ Noll, Walter (April 2007). "On the Concept of Force" (PDF). Carnegie Mellon University. Retrieved 28 October 2013.
  15. ^ C. Hellingman (1992). "Newton's third law revisited". Phys. Educ. 27 (2): 112–115. Bibcode:1992PhyEd..27..112H. doi:10.1088/0031-9120/27/2/011. Quoting Newton in the Principia: It is not one action by which the Sun attracts Jupiter, and another by which Jupiter attracts the Sun; but it is one action by which the Sun and Jupiter mutually endeavour to come nearer together.
  16. ^ Dr. Nikitin (2007). "Dynamics of translational motion". Retrieved 2008-01-04.
  17. ^ a b c d e Cutnell & Johnson 2003
  18. ^ "Seminar: Visualizing Special Relativity". The Relativistic Raytracer. Retrieved 2008-01-04.
  19. ^ Wilson, John B. "Four-Vectors (4-Vectors) of Special Relativity: A Study of Elegant Physics". The Science Realm: John's Virtual Sci-Tech Universe. Archived from the original on 26 June 2009. Retrieved 2008-01-04.
  20. ^ "Introduction to Free Body Diagrams". Physics Tutorial Menu. University of Guelph. Archived from the original on 2008-01-16. Retrieved 2008-01-02.
  21. ^ Henderson, Tom (2004). "The Physics Classroom". The Physics Classroom and Mathsoft Engineering & Education, Inc. Archived from the original on 2008-01-01. Retrieved 2008-01-02.
  22. ^ "Static Equilibrium". Physics Static Equilibrium (forces and torques). University of the Virgin Islands. Archived from the original on October 19, 2007. Retrieved 2008-01-02.
  23. ^ a b Shifman, Mikhail (1999). ITEP lectures on particle physics and field theory. World Scientific. ISBN 978-981-02-2639-8.
  24. ^ Nave, Carl Rod. "Pauli Exclusion Principle". HyperPhysics. University of Guelph. Retrieved 2013-10-28.
  25. ^ "Fermions & Bosons". The Particle Adventure. Archived from the original on 2007-12-18. Retrieved 2008-01-04.
  26. ^ "Standard model of particles and interactions". Contemporary Physics Education Project. 2000. Retrieved 2 January 2017.
  27. ^ Cook, A.H. (1965). "A New Absolute Determination of the Acceleration due to Gravity at the National Physical Laboratory". Nature. 208 (5007): 279. Bibcode:1965Natur.208..279C. doi:10.1038/208279a0.
  28. ^ a b Young, Hugh; Freedman, Roger; Sears, Francis and Zemansky, Mark (1949) University Physics. Pearson Education. pp. 59–82
  29. ^ "Sir Isaac Newton: The Universal Law of Gravitation". Astronomy 161 The Solar System. Retrieved 2008-01-04.
  30. ^ Watkins, Thayer. "Perturbation Analysis, Regular and Singular". Department of Economics. San José State University.
  31. ^ Kollerstrom, Nick (2001). "Neptune's Discovery. The British Case for Co-Prediction". University College London. Archived from the original on 2005-11-11. Retrieved 2007-03-19.
  32. ^ "Powerful New Black Hole Probe Arrives at Paranal". Retrieved 13 August 2015.
  33. ^ Siegel, Ethan (20 May 2016). "When Did Isaac Newton Finally Fail?". Forbes. Retrieved 3 January 2017.
  34. ^ Coulomb, Charles (1784). "Recherches théoriques et expérimentales sur la force de torsion et sur l'élasticité des fils de metal". Histoire de l'Académie Royale des Sciences: 229–269.
  35. ^ a b c Feynman volume 2
  36. ^ Scharf, Toralf (2007). Polarized light in liquid crystals and polymers. John Wiley and Sons. p. 19. ISBN 978-0-471-74064-3., Chapter 2, p. 19
  37. ^ Duffin, William (1980). Electricity and Magnetism, 3rd Ed. McGraw-Hill. pp. 364–383. ISBN 978-0-07-084111-6.
  38. ^ Stevens, Tab (10 July 2003). "Quantum-Chromodynamics: A Definition – Science Articles". Archived from the original on 2011-10-16. Retrieved 2008-01-04.
  39. ^ "Tension Force". Non-Calculus Based Physics I. Retrieved 2008-01-04.
  40. ^ Fitzpatrick, Richard (2006-02-02). "Strings, pulleys, and inclines". Retrieved 2008-01-04.
  41. ^ Nave, Carl Rod. "Elasticity". HyperPhysics. University of Guelph. Retrieved 2013-10-28.
  42. ^ Mallette, Vincent (1982–2008). "The Coriolis Force". Publications in Science and Mathematics, Computing and the Humanities. Inwit Publishing, Inc. Retrieved 2008-01-04.
  43. ^ Nave, Carl Rod. "Newton's 2nd Law: Rotation". HyperPhysics. University of Guelph. Retrieved 2013-10-28.
  44. ^ Fitzpatrick, Richard (2007-01-07). "Newton's third law of motion". Retrieved 2008-01-04.
  45. ^ Nave, Carl Rod. "Centripetal Force". HyperPhysics. University of Guelph. Retrieved 2013-10-28.
  46. ^ Hibbeler, Russell C. (2010). Engineering Mechanics, 12th edition. Pearson Prentice Hall. p. 222. ISBN 978-0-13-607791-6.
  47. ^ Singh, Sunil Kumar (2007-08-25). "Conservative force". Connexions. Retrieved 2008-01-04.
  48. ^ Davis, Doug. "Conservation of Energy". General physics. Retrieved 2008-01-04.
  49. ^ a b c d e Wandmacher, Cornelius; Johnson, Arnold (1995). Metric Units in Engineering. ASCE Publications. p. 15. ISBN 978-0-7844-0070-8.

Further reading

  • Corben, H.C.; Philip Stehle (1994). Classical Mechanics. New York: Dover publications. pp. 28–31. ISBN 978-0-486-68063-7.
  • Cutnell, John D.; Johnson, Kenneth W. (2003). Physics, Sixth Edition. Hoboken, New Jersey: John Wiley & Sons Inc. ISBN 978-0471151838.
  • Feynman, Richard P.; Leighton; Sands, Matthew (2010). The Feynman lectures on physics. Vol. I: Mainly mechanics, radiation and heat (New millennium ed.). New York: BasicBooks. ISBN 978-0465024933.
  • Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew (2010). The Feynman lectures on physics. Vol. II: Mainly electromagnetism and matter (New millennium ed.). New York: BasicBooks. ISBN 978-0465024940.
  • Halliday, David; Resnick, Robert; Krane, Kenneth S. (2001). Physics v. 1. New York: John Wiley & Sons. ISBN 978-0-471-32057-9.
  • Kleppner, Daniel; Kolenkow, Robert J. (2010). An introduction to mechanics (3. print ed.). Cambridge: Cambridge University Press. ISBN 978-0521198219.
  • Parker, Sybil (1993). "force". Encyclopedia of Physics. Ohio: McGraw-Hill. p. 107. ISBN 978-0-07-051400-3.
  • Sears F., Zemansky M. & Young H. (1982). University Physics. Reading, Massachusetts: Addison-Wesley. ISBN 978-0-201-07199-3.
  • Serway, Raymond A. (2003). Physics for Scientists and Engineers. Philadelphia: Saunders College Publishing. ISBN 978-0-534-40842-8.
  • Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.). W.H. Freeman. ISBN 978-0-7167-0809-4.
  • Verma, H.C. (2004). Concepts of Physics Vol 1 (2004 Reprint ed.). Bharti Bhavan. ISBN 978-8177091878.

External links

Area 51

The United States Air Force facility commonly known as Area 51 is a highly classified remote detachment of Edwards Air Force Base, within the Nevada Test and Training Range. According to the Central Intelligence Agency (CIA), the correct names for the facility are Homey Airport (ICAO: KXTA) and Groom Lake, though the name Area 51 was used in a CIA document from the Vietnam War. The facility has also been referred to as Dreamland and Paradise Ranch, among other nicknames. USAF public relations has referred to the facility as "an operating location near Groom Dry Lake". The special use airspace around the field is referred to as Restricted Area 4808 North (R-4808N).The base's current primary purpose is publicly unknown; however, based on historical evidence, it most likely supports the development and testing of experimental aircraft and weapons systems (black projects). The intense secrecy surrounding the base has made it the frequent subject of conspiracy theories and a central component to unidentified flying object (UFO) folklore. Although the base has never been declared a secret base, all research and occurrences in Area 51 are Top Secret/Sensitive Compartmented Information (TS/SCI). On 25 June 2013, following a Freedom of Information Act (FOIA) request filed in 2005, the CIA publicly acknowledged the existence of the base for the first time, declassifying documents detailing the history and purpose of Area 51.Area 51 is located in the southern portion of Nevada in the western United States, 83 miles (134 km) north-northwest of Las Vegas. Situated at its center, on the southern shore of Groom Lake, is a large military airfield. The site was acquired by the United States Air Force in 1955, primarily for the flight testing of the Lockheed U-2 aircraft. The area around Area 51, including the small town of Rachel on the "Extraterrestrial Highway", is a popular tourist destination.

Darth Vader

Darth Vader is a fictional character in the Star Wars franchise. He is a primary antagonist in the original trilogy, but, as Anakin Skywalker, is the main protagonist of the prequel trilogy. Star Wars creator George Lucas has collectively referred to the first six episodic films of the franchise as "the tragedy of Darth Vader."Originally a Jedi prophesied to bring balance to the Force, Anakin Skywalker is lured to the dark side of the Force by Palpatine, who is secretly a Sith Lord. After fighting a lightsaber battle with his former mentor Obi-Wan Kenobi in which he is dismembered, Vader is transformed into a cyborg. He then serves the Galactic Empire as Darth Vader until he redeems himself by saving his son, Luke Skywalker, from Palpatine, sacrificing his own life in the process. He is also the father of Princess Leia, the secret husband of Padmé Amidala, and grandfather of Kylo Ren, the main villain of the Star Wars sequel trilogy.

The character has been portrayed by numerous actors. His cinematic appearances span the first six Star Wars films, as well as Rogue One, and he is referenced in both The Force Awakens and The Last Jedi. He also appears in television series (most substantially The Clone Wars) and numerous iterations of the Star Wars Expanded Universe, including video games, novels, and comic books.

Darth Vader has become one of the most iconic villains in popular culture, and has been listed among the greatest villains and fictional characters ever. The American Film Institute listed him as the third greatest movie villain in cinema history on 100 Years... 100 Heroes and Villains, behind Hannibal Lecter and Norman Bates. His role as a tragic hero in the prequel trilogy was met with positive reviews.

General Dynamics F-16 Fighting Falcon

The General Dynamics F-16 Fighting Falcon is a single-engine supersonic multirole fighter aircraft originally developed by General Dynamics (now Lockheed Martin) for the United States Air Force (USAF). Designed as an air superiority day fighter, it evolved into a successful all-weather multirole aircraft. Over 4,600 aircraft have been built since production was approved in 1976. Although no longer being purchased by the U.S. Air Force, improved versions are being built for export customers. In 1993, General Dynamics sold its aircraft manufacturing business to the Lockheed Corporation, which in turn became part of Lockheed Martin after a 1995 merger with Martin Marietta.The Fighting Falcon's key features include a frameless bubble canopy for better visibility, side-mounted control stick to ease control while maneuvering, an ejection seat reclined 30 degrees from vertical to reduce the effect of g-forces on the pilot, and the first use of a relaxed static stability/fly-by-wire flight control system which helps to make it a nimble aircraft. The F-16 has an internal M61 Vulcan cannon and 11 locations for mounting weapons and other mission equipment. The F-16's official name is "Fighting Falcon", but "Viper" is commonly used by its pilots and crews, due to a perceived resemblance to a viper snake as well as the Colonial Viper starfighter on Battlestar Galactica which aired around when the F-16 entered service.In addition to active duty in the U.S. Air Force, Air Force Reserve Command, and Air National Guard units, the aircraft is also used by the USAF aerial demonstration team, the U.S. Air Force Thunderbirds, and as an adversary/aggressor aircraft by the United States Navy. The F-16 has also been procured to serve in the air forces of 25 other nations. As of 2015, it is the world's most numerous fixed-wing aircraft in military service.

Gravity

Gravity (from Latin gravitas, meaning 'weight'), or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the ocean tides. The gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing, forming stars – and for the stars to group together into galaxies – so gravity is responsible for many of the large-scale structures in the Universe. Gravity has an infinite range, although its effects become increasingly weaker on farther objects.

Gravity is most accurately described by the general theory of relativity (proposed by Albert Einstein in 1915) which describes gravity not as a force, but as a consequence of the curvature of spacetime caused by the uneven distribution of mass. The most extreme example of this curvature of spacetime is a black hole, from which nothing—not even light—can escape once past the black hole's event horizon. However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force which causes any two bodies to be attracted to each other, with the force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Gravity is the weakest of the four fundamental forces of physics, approximately 1038 times weaker than the strong force, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak force. As a consequence, it has no significant influence at the level of subatomic particles. In contrast, it is the dominant force at the macroscopic scale, and is the cause of the formation, shape and trajectory (orbit) of astronomical bodies. For example, gravity causes the Earth and the other planets to orbit the Sun, it also causes the Moon to orbit the Earth, and causes the formation of tides, the formation and evolution of the Solar System, stars and galaxies.

The earliest instance of gravity in the Universe, possibly in the form of quantum gravity, supergravity or a gravitational singularity, along with ordinary space and time, developed during the Planck epoch (up to 10−43 seconds after the birth of the Universe), possibly from a primeval state, such as a false vacuum, quantum vacuum or virtual particle, in a currently unknown manner. Attempts to develop a theory of gravity consistent with quantum mechanics, a quantum gravity theory, which would allow gravity to be united in a common mathematical framework (a theory of everything) with the other three forces of physics, are a current area of research.

Indian Air Force

The Indian Air Force (IAF) is the air arm of the Indian Armed Forces. Its complement of personnel and aircraft assets ranks fourth amongst the air forces of the world. Its primary mission is to secure Indian airspace and to conduct aerial warfare during armed conflict. It was officially established on 8 October 1932 as an auxiliary air force of the British Empire which honoured India's aviation service during World War II with the prefix Royal. After India gained independence from the United Kingdom in 1947, the name Royal Indian Air Force was kept and served in the name of Dominion of India. With the government's transition to a Republic in 1950, the prefix Royal was removed after only three years.

Since 1950 the IAF has been involved in four wars with neighboring Pakistan and one with the People's Republic of China. Other major operations undertaken by the IAF include Operation Vijay, Operation Meghdoot, Operation Cactus and Operation Poomalai. The IAF's mission expands beyond engagement with hostile forces, with the IAF participating in United Nations peacekeeping missions.

The President of India holds the rank of Supreme Commander of the IAF. As of 1 July 2017, 139,576 personnel are in service with the Indian Air Force. The Chief of Air Staff, an air chief marshal, is a four-star officer and is responsible for the bulk of operational command of the Air Force. There is never more than one serving ACM at any given time in the IAF. The rank of Marshal of the Air Force has been conferred by the President of India on one occasion in history, to Arjan Singh. On 26 January 2002 Singh became the first and so far, only five-star rank officer of the IAF.

Israel Defense Forces

The Israel Defense Forces (IDF; Hebrew: צְבָא הַהֲגָנָה לְיִשְׂרָאֵל Tsva ha-Hagana le-Yisra'el, lit. "The Army of Defense for Israel"; Arabic: جيش الدفاع الإسرائيلي‎), commonly known in Israel by the Hebrew acronym Tzahal (צה״ל), are the military forces of the State of Israel. They consist of the ground forces, air force, and navy. It is the sole military wing of the Israeli security forces, and has no civilian jurisdiction within Israel. The IDF is headed by its Chief of General Staff, the Ramatkal, subordinate to the Defense Minister of Israel; Lieutenant General (Rav Aluf) Aviv Kochavi has served as Chief of Staff since January 15, 2019.

An order from Defense Minister David Ben-Gurion on 26 May 1948 officially set up the Israel Defense Forces as a conscript army formed out of the paramilitary group Haganah, incorporating the militant groups Irgun and Lehi. The IDF served as Israel's armed forces in all the country's major military operations—including the 1948 War of Independence, 1951–1956 Retribution operations, 1956 Sinai War, 1964–1967 War over Water, 1967 Six-Day War, 1967–1970 War of Attrition, 1968 Battle of Karameh, 1973 Operation Spring of Youth, 1973 Yom Kippur War, 1976 Operation Entebbe, 1978 Operation Litani, 1982 Lebanon War, 1982–2000 South Lebanon conflict, 1987–1993 First Intifada, 2000–2005 Second Intifada, 2002 Operation Defensive Shield, 2006 Lebanon War, 2008–2009 Operation Cast Lead, 2012 Operation Pillar of Defense, and 2014 Operation Protective Edge. According to GlobalSecurity.org, the number of wars and border conflicts in which the IDF has been involved in its short history makes it one of the most battle-trained armed forces in the world. While originally the IDF operated on three fronts—against Lebanon and Syria in the north, Jordan and Iraq in the east, and Egypt in the south—after the 1979 Egyptian–Israeli Peace Treaty, it has concentrated its activities in southern Lebanon and the Palestinian Territories, including the First and the Second Intifada.

The Israel Defense Forces is somewhat unique in its inclusion of mandatory conscription of women and its structure, which emphasizes close relations between the army, navy, and air force. Since its founding, the IDF has been specifically designed to match Israel's unique security situation. The IDF is one of Israeli society's most prominent institutions, influencing the country's economy, culture and political scene. In 1965, the Israel Defense Forces was awarded the Israel Prize for its contribution to education. The IDF uses several technologies developed in Israel, many of them made specifically to match the IDF's needs, such as the Merkava main battle tank, Achzarit armoured personnel carrier, high tech weapons systems, the Iron Dome missile defense system, Trophy active protection system for vehicles, and the Galil and Tavor assault rifles. The Uzi submachine gun was invented in Israel and used by the IDF until December 2003, ending a service that began in 1954. Since 1967, the IDF has had close military relations with the United States, including development cooperation, such as on the F-15I jet, THEL laser defense system, and the Arrow missile defense system.

The Israel Defense Forces are believed to have had an operational nuclear weapons capability since 1967, possibly possessing between 80 and 400 nuclear weapons, with delivery systems forming a nuclear triad, of plane launched-missiles, Jericho III intercontinental ballistic missiles and submarine launched cruise missiles.

Lockheed Martin F-22 Raptor

The Lockheed Martin F-22 Raptor is a fifth-generation, single-seat, twin-engine, all-weather stealth tactical fighter aircraft developed for the United States Air Force (USAF). The result of the USAF's Advanced Tactical Fighter program, the aircraft was designed primarily as an air superiority fighter, but also has ground attack, electronic warfare, and signal intelligence capabilities. The prime contractor, Lockheed Martin, built most of the F-22's airframe and weapons systems and conducted final assembly, while Boeing provided the wings, aft fuselage, avionics integration, and training systems.

The aircraft was variously designated F-22 and F/A-22 before it formally entered service in December 2005 as the F-22A. After a protracted development and despite operational issues, the USAF considered the F-22 critical to its tactical air power. When the aircraft was introduced, the USAF stated that it was unmatched by any known or projected fighter. The F-22's combination of stealth, aerodynamic performance, and situational awareness gives the aircraft unprecedented air combat capabilities.The high cost of the aircraft, a lack of clear air-to-air missions due to delays in Russian and Chinese fighter programs, a ban on exports, and development of the more versatile F-35 led to the end of F-22 production. A final procurement tally of 187 operational production aircraft was established in 2009, and the last F-22 was delivered to the USAF in 2012.

Lockheed Martin F-35 Lightning II

The Lockheed Martin F-35 Lightning II is a family of single-seat, single-engine, all-weather stealth multirole fighters. The fifth-generation combat aircraft is designed to perform ground-attack and air-superiority missions. It has three main models: the F-35A conventional takeoff and landing (CTOL) variant, the F-35B short take-off and vertical-landing (STOVL) variant, and the F-35C carrier-based catapult-assisted take-off but arrested recovery (CATOBAR) variant. The F-35 descends from the Lockheed Martin X-35, the winning design of the Joint Strike Fighter (JSF) program. It is built by Lockheed Martin and many subcontractors, including Northrop Grumman, Pratt & Whitney, and BAE Systems.

The United States principally funds F-35 development, with additional funding from other NATO members and close U.S. allies, including the United Kingdom, Italy, Australia, Canada, Norway, Denmark, the Netherlands, and Turkey. These funders generally receive subcontracts to manufacture components for the aircraft; for example, Turkey is the sole supplier of several F-35 parts. Several other countries have ordered, or are considering ordering, the aircraft.

As the largest and most expensive military program ever, the F-35 became the subject of much scrutiny and criticism in the U.S. and in other countries. In 2013 and 2014, critics argued that the plane was "plagued with design flaws", with many blaming the procurement process in which Lockheed was allowed "to design, test, and produce the F-35 all at the same time," instead of identifying and fixing "defects before firing up its production line". By 2014, the program was "$163 billion over budget [and] seven years behind schedule". Critics also contend that the program's high sunk costs and political momentum make it "too big to kill".The F-35 first flew on 15 December 2006. In July 2015, the United States Marines declared its first squadron of F-35B fighters ready for deployment. However, the DOD-based durability testing indicated the service life of early-production F-35B aircraft is well under the expected 8,000 flight hours, and may be as low as 2,100 flight hours. Lot 9 and later aircraft include design changes but service life testing has yet to occur. The U.S. Air Force declared its first squadron of F-35As ready for deployment in August 2016. The U.S. Navy declared its first F-35Cs ready in February 2019. In 2018, the F-35 made its combat debut with the Israeli Air Force.The U.S. plans to buy 2,663 F-35s, which will provide the bulk of the crewed tactical airpower of the U.S. Air Force, Navy, and Marine Corps in coming decades. Deliveries of the F-35 for the U.S. military are scheduled until 2037 with a projected service life up to 2070.

Magnetic field

A magnetic field is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials. Magnetic fields are observed in a wide range of size scales, from subatomic particles to galaxies. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials (such as iron) and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges (electric currents) such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field vary with location. As such, it is an example of a vector field.

The term 'magnetic field' is used for two distinct but closely related fields denoted by the symbols B and H. In the International System of Units, H, magnetic field strength, is measured in the SI base units of ampere per meter. B, magnetic flux density, is measured in tesla (in SI base units: kilogram per second2 per ampere), which is equivalent to newton per meter per ampere. H and B differ in how they account for magnetization. In a vacuum, B and H are the same aside from units; but in a magnetized material, B/ and H differ by the magnetization M of the material at that point in the material.

Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated, and are both components of the electromagnetic force, one of the four fundamental forces of nature.

Magnetic fields are widely used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.

Newton's laws of motion

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a quantitative measure of the force, and the third asserts that a single isolated force doesn't exist. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows:

The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687. Newton used them to explain and investigate the motion of many physical objects and systems. For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.

A fourth law is often also described in the bibliography, which states that forces add up like vectors, that is, that forces obey the principle of superposition.

Royal Air Force

The Royal Air Force (RAF) is the United Kingdom's aerial warfare force. Formed towards the end of the First World War on 1 April 1918, it is the oldest independent air force in the world. Following victory over the Central Powers in 1918 the RAF emerged as, at the time, the largest air force in the world. Since its formation, the RAF has taken a significant role in British military history. In particular, it played a large part in the Second World War where it fought its most famous campaign, the Battle of Britain.The RAF's mission is to support the objectives of the British Ministry of Defence (MoD), which are to "provide the capabilities needed to ensure the security and defence of the United Kingdom and overseas territories, including against terrorism; to support the Government's foreign policy objectives particularly in promoting international peace and security". The RAF describes its mission statement as "... [to provide] an agile, adaptable and capable Air Force that, person for person, is second to none, and that makes a decisive air power contribution in support of the UK Defence Mission". The mission statement is supported by the RAF's definition of air power, which guides its strategy. Air power is defined as "the ability to project power from the air and space to influence the behaviour of people or the course of events".Today the Royal Air Force maintains an operational fleet of various types of aircraft, described by the RAF as being "leading-edge" in terms of technology. This largely consists of fixed-wing aircraft, including: fighter and strike aircraft, airborne early warning and control aircraft, ISTAR and SIGINT aircraft, aerial refueling aircraft and strategic and tactical transport aircraft. The majority of the RAF's rotary-wing aircraft form part of the tri-service Joint Helicopter Command in support of ground forces. Most of the RAF's aircraft and personnel are based in the UK, with many others serving on operations (principally over Iraq and Syria) or at long-established overseas bases (Ascension Island, Cyprus, Gibraltar, and the Falkland Islands). Although the RAF is the principal British air power arm, the Royal Navy's Fleet Air Arm and the British Army's Army Air Corps also deliver air power which is integrated into the maritime, littoral and land environments.

Royal Australian Air Force

The Royal Australian Air Force (RAAF), formed March 1921, is the aerial warfare branch of the Australian Defence Force (ADF). It operates the majority of the ADF's fixed wing aircraft, although both the Australian Army and Royal Australian Navy also operate aircraft in various roles. It directly continues the traditions of the Australian Flying Corps (AFC), formed on 22 October 1912. The RAAF provides support across a spectrum of operations such as air superiority, precision strikes, intelligence, surveillance and reconnaissance, air mobility, space surveillance, and humanitarian support.

The RAAF took part in many of the 20th century's major conflicts. During the early years of the Second World War a number of RAAF bomber, fighter, reconnaissance and other squadrons served in Britain, and with the Desert Air Force located in North Africa and the Mediterranean. From 1942, a large number of RAAF units were formed in Australia, and fought in South West Pacific Area. Thousands of Australians also served with other Commonwealth air forces in Europe, including during the bomber offensive against Germany. By the time the war ended, a total of 216,900 men and women served in the RAAF, of whom 10,562 were killed in action.Later the RAAF served in the Berlin Airlift, Korean War, Malayan Emergency, Indonesia–Malaysia Confrontation and Vietnam War. More recently, the RAAF has participated in operations in East Timor, the Iraq War, the War in Afghanistan, and the military intervention against the Islamic State of Iraq and the Levant (ISIL).

The RAAF has 259 aircraft, of which 110 are combat aircraft.

Star Wars

Star Wars is an American epic space-opera media franchise created by George Lucas. The franchise began with the eponymous 1977 film and quickly became a worldwide pop-culture phenomenon.

The first film, later subtitled Episode IV – A New Hope, was followed by two sequels, Episode V – The Empire Strikes Back (1980) and Episode VI – Return of the Jedi (1983), collectively referred to as the original trilogy. A subsequent prequel trilogy, consisting of Episode I – The Phantom Menace (1999), Episode II – Attack of the Clones (2002) and Episode III – Revenge of the Sith (2005), completed what Lucas later called the "tragedy of Darth Vader". Finally, a sequel trilogy began with Episode VII – The Force Awakens (2015), continued with Episode VIII – The Last Jedi (2017), and will conclude with Episode IX – The Rise of Skywalker (2019). The first eight films were nominated for Academy Awards (with wins going to the first two released) and were commercially successful. Together with the theatrical anthology films Rogue One: A Star Wars Story (2016) and Solo: A Star Wars Story (2018), the films combined box office revenue equates to over US$9 billion, and is currently the second-highest-grossing film franchise.The film series expanded into other media, including television series, video games, novels, comic books, theme park attractions and themed areas, resulting in an all encompassing fictional universe. Star Wars holds a Guinness World Records title for the "Most successful film merchandising franchise". In 2018, the total value of the Star Wars franchise was estimated at US$65 billion, and it is currently the fifth-highest-grossing media franchise of all-time.

Torque

Torque, moment, or moment of force is the rotational equivalent of linear force. The concept originated with the studies of Archimedes on the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object. The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.

In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector connecting the origin to the point of force application, and the angle between the force and lever arm vectors. In symbols:

where

is the torque vector and is the magnitude of the torque,
r is the position vector (a vector from the origin of the coordinate system defined to the point where the force is applied)
F is the force vector,
× denotes the cross product, which is defined as magnitudes of the respective vectors times .
is the angle between the force vector and the lever arm vector.

The SI unit for torque is N⋅m. For more on the units of torque, see Units.

United States Air Force

The United States Air Force (USAF) is the aerial and space warfare service branch of the United States Armed Forces. It is one of the five branches of the United States Armed Forces, and one of the seven American uniformed services. Initially formed as a part of the United States Army on 1 August 1907, the USAF was established as a separate branch of the U.S. Armed Forces on 18 September 1947 with the passing of the National Security Act of 1947. It is the youngest branch of the U.S. Armed Forces, and the fourth in order of precedence. The USAF is the largest and most technologically advanced air force in the world. The Air Force articulates its core missions as air and space superiority, global integrated intelligence, surveillance, and reconnaissance, rapid global mobility, global strike, and command and control.

The U.S. Air Force is a military service branch organized within the Department of the Air Force, one of the three military departments of the Department of Defense. The Air Force, through the Department of the Air Force, is headed by the civilian Secretary of the Air Force, who reports to the Secretary of Defense, and is appointed by the President with Senate confirmation. The highest-ranking military officer in the Air Force is the Chief of Staff of the Air Force, who exercises supervision over Air Force units and serves as one of the Joint Chiefs of Staff. Air Force components are assigned, as directed by the Secretary of Defense, to the combatant commands, and neither the Secretary of the Air Force nor the Chief of Staff of the Air Force have operational command authority over them.

Along with conducting independent air and space operations, the U.S. Air Force provides air support for land and naval forces and aids in the recovery of troops in the field. As of 2017, the service operates more than 5,369 military aircraft, 406 ICBMs and 170 military satellites. It has a $161 billion budget and is the second largest service branch, with 321,444 active duty airmen, 141,800 civilian personnel, 69,200 reserve airmen, and 105,700 Air National Guard airmen.

United States Armed Forces

The United States Armed Forces are the military forces of the United States of America. It consists of the Army, Marine Corps, Navy, Air Force, and Coast Guard. The President of the United States is the Commander-in-Chief of the Armed Forces and forms military policy with the Department of Defense (DoD) and Department of Homeland Security (DHS), both federal executive departments, acting as the principal organs by which military policy is carried out. All five armed services are among the seven uniformed services of the United States.From the time of its inception, the U.S. Armed Forces played a decisive role in the history of the United States. A sense of national unity and identity was forged as a result of victory in the First Barbary War and the Second Barbary War. Even so, the founders of the United States were suspicious of a permanent military force. It played a critical role in the American Civil War, continuing to serve as the armed forces of the United States, although a number of its officers resigned to join the military of the Confederate States. The National Security Act of 1947, adopted following World War II and during the Cold War's onset, created the modern U.S. military framework. The Act established the National Military Establishment, headed by the Secretary of Defense; and created the Department of the Air Force and the National Security Council. It was amended in 1949, renaming the National Military Establishment the Department of Defense, and merged the cabinet-level Department of the Army, Department of the Navy, and Department of the Air Force, into the Department of Defense.

The U.S. Armed Forces are one of the largest militaries in terms of the number of personnel. It draws its personnel from a large pool of paid volunteers. Although conscription has been used in the past in various times of both war and peace, it has not been used since 1973, but the Selective Service System retains the power to conscript males, and requires that all male citizens and residents residing in the U.S. between the ages of 18–25 register with the service. On February 22, 2019, however, a federal judge ruled that registering only males for Selective Service is unconstitutional.

As of 2017, the U.S. spends about US$610 billion annually to fund its military forces and Overseas Contingency Operations. Put together, the U.S. constitutes roughly 40 percent of the world's military expenditures. The U.S. Armed Forces has significant capabilities in both defense and power projection due to its large budget, resulting in advanced and powerful technologies which enables a widespread deployment of the force around the world, including around 800 military bases outside the United States. The U.S. Air Force is the world's largest air force, the U.S. Navy is the world's largest navy by tonnage, and the U.S. Navy and the U.S. Marine Corps combined are the world's second largest air arm. In terms of size, the U.S. Coast Guard is the world's 12th largest naval force.

United States Army

The United States Army (USA) is the land warfare service branch of the United States Armed Forces. It is one of the seven uniformed services of the United States, and is designated as the Army of the United States in the United States Constitution. As the oldest and most senior branch of the U.S. military in order of precedence, the modern U.S. Army has its roots in the Continental Army, which was formed (14 June 1775) to fight the American Revolutionary War (1775–1783)—before the United States of America was established as a country. After the Revolutionary War, the Congress of the Confederation created the United States Army on 3 June 1784 to replace the disbanded Continental Army. The United States Army considers itself descended from the Continental Army, and dates its institutional inception from the origin of that armed force in 1775.As a uniformed military service, the U.S. Army is part of the Department of the Army, which is one of the three military departments of the Department of Defense. The U.S. Army is headed by a civilian senior appointed civil servant, the Secretary of the Army (SECARMY) and by a chief military officer, the Chief of Staff of the Army (CSA) who is also a member of the Joint Chiefs of Staff. It is the largest military branch, and in the fiscal year 2017, the projected end strength for the Regular Army (USA) was 476,000 soldiers; the Army National Guard (ARNG) had 343,000 soldiers and the United States Army Reserve (USAR) had 199,000 soldiers; the combined-component strength of the U.S. Army was 1,018,000 soldiers. As a branch of the armed forces, the mission of the U.S. Army is "to fight and win our Nation's wars, by providing prompt, sustained, land dominance, across the full range of military operations and the spectrum of conflict, in support of combatant commanders". The branch participates in conflicts worldwide and is the major ground-based offensive and defensive force of the United States.

United States Navy

The United States Navy (USN) is the naval warfare service branch of the United States Armed Forces and one of the seven uniformed services of the United States. It is the largest and most capable navy in the world and it has been estimated that in terms of tonnage of its active battle fleet alone, it is larger than the next 13 navies combined, which includes 11 U.S. allies or partner nations. with the highest combined battle fleet tonnage and the world's largest aircraft carrier fleet, with eleven in service, and two new carriers under construction. With 319,421 personnel on active duty and 99,616 in the Ready Reserve, the Navy is the third largest of the service branches. It has 282 deployable combat vessels and more than 3,700 operational aircraft as of March 2018, making it the second-largest air force in the world, after the United States Air Force.

The U.S. Navy traces its origins to the Continental Navy, which was established during the American Revolutionary War and was effectively disbanded as a separate entity shortly thereafter. The U.S. Navy played a major role in the American Civil War by blockading the Confederacy and seizing control of its rivers. It played the central role in the World War II defeat of Imperial Japan. The US Navy emerged from World War II as the most powerful navy in the world. The 21st century U.S. Navy maintains a sizable global presence, deploying in strength in such areas as the Western Pacific, the Mediterranean, and the Indian Ocean. It is a blue-water navy with the ability to project force onto the littoral regions of the world, engage in forward deployments during peacetime and rapidly respond to regional crises, making it a frequent actor in U.S. foreign and military policy.

The Navy is administratively managed by the Department of the Navy, which is headed by the civilian Secretary of the Navy. The Department of the Navy is itself a division of the Department of Defense, which is headed by the Secretary of Defense. The Chief of Naval Operations (CNO) is the most senior naval officer serving in the Department of the Navy.

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