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90-424: A ballistic body is a free-moving body with momentum which can be subject to forces such as the forces exerted by pressurized gases from a gun barrel or a propelling nozzle , normal force by rifling , and gravity and air drag during flight. A ballistic missile is a missile that is guided only during the relatively brief initial phase of powered flight and the trajectory is subsequently governed by

180-402: A n t . {\displaystyle m_{A}v_{A}+m_{B}v_{B}+m_{C}v_{C}+...=constant.} This conservation law applies to all interactions, including collisions (both elastic and inelastic ) and separations caused by explosive forces. It can also be generalized to situations where Newton's laws do not hold, for example in the theory of relativity and in electrodynamics . Momentum

270-418: A Galilean transformation . If a particle is moving at speed ⁠ d x / d t ⁠ = v in the first frame of reference, in the second, it is moving at speed v ′ = d x ′ d t = v − u . {\displaystyle v'={\frac {{\text{d}}x'}{{\text{d}}t}}=v-u\,.} Since u does not change,

360-407: A commercial industry involved in the research and development , engineering , production, and servicing of military material, equipment, and facilities. Many industrialized countries have a domestic arms industry to supply their own military forces, and some also have a substantial trade in weapons for use by their citizens for self-defense, hunting, or sporting purposes. Contracts to supply

450-516: A momentum density can be defined as momentum per volume (a volume-specific quantity ). A continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids. Momentum is a vector quantity : it has both magnitude and direction. Since momentum has a direction, it can be used to predict

540-752: A 1 kg model airplane, traveling due north at 1 m/s in straight and level flight, has a momentum of 1 kg⋅m/s due north measured with reference to the ground. The momentum of a system of particles is the vector sum of their momenta. If two particles have respective masses m 1 and m 2 , and velocities v 1 and v 2 , the total momentum is p = p 1 + p 2 = m 1 v 1 + m 2 v 2 . {\displaystyle {\begin{aligned}p&=p_{1}+p_{2}\\&=m_{1}v_{1}+m_{2}v_{2}\,.\end{aligned}}} The momenta of more than two particles can be added more generally with

630-402: A collision. For example, suppose there are two bodies of equal mass m , one stationary and one approaching the other at a speed v (as in the figure). The center of mass is moving at speed ⁠ v / 2 ⁠ and both bodies are moving towards it at speed ⁠ v / 2 ⁠ . Because of the symmetry, after the collision both must be moving away from the center of mass at

720-418: A court or other part of a legal system. Separately from ballistics information, firearm and tool mark examinations (" ballistic fingerprinting ") involve analyzing firearm, ammunition, and tool mark evidence in order to establish whether a certain firearm or tool was used in the commission of a crime. Astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning

810-405: A given country's military are awarded by governments, making arms contracts of substantial political importance. The link between politics and the arms trade can result in the development of a " military–industrial complex ", where the armed forces, commerce, and politics become closely linked. According to research institute SIPRI, the volume of international transfers of major weapons in 2010–2014

900-858: A major driver of cultural evolution and human history up to today since weapons are a type of tool that is used to dominate and subdue autonomous agents such as animals and, by doing so, allow for an expansion of the cultural niche, while simultaneously other weapon users (i.e., agents such as humans, groups, and cultures) are able to adapt to the weapons of enemies by learning, triggering a continuous process of competitive technological, skill, and cognitive improvement ( arms race ). The use of objects as weapons has been observed among chimpanzees , leading to speculation that early hominids used weapons as early as five million years ago. However, this cannot be confirmed using physical evidence because wooden clubs, spears, and unshaped stones would have left an ambiguous record. The earliest unambiguous weapons to be found are

990-466: A number of issues around the potential ongoing risks from deployed weapons, the safe storage of weapons, and their eventual disposal when they are no longer effective or safe. Strange and exotic weapons are a recurring feature or theme in science fiction . In some cases, weapons first introduced in science fiction have now become a reality. Other science fiction weapons, such as force fields and stasis fields , remain purely fictional and are often beyond

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1080-433: A sub-field of ballistics, is the study of the propulsion of a projectile . In guns , internal ballistics covers the time from the propellant 's ignition until the projectile exits the gun barrel . The study of internal ballistics is important to designers and users of firearms of all types, from small-bore rifles and pistols , to high-tech artillery . For rocket propelled projectiles, internal ballistics covers

1170-617: A worldwide crusade in the 1920s. Poison gas did not win battles, and the generals did not want it. The soldiers hated it far more intensely than bullets or explosive shells. By 1918, chemical shells made up 35 percent of French ammunition supplies, 25 percent of British, and 20 percent of American stock. The “Protocol for the Prohibition of the Use in War of Asphyxiating, Poisonous, or Other Gases and of Bacteriological Methods of Warfare”, also known as

1260-413: Is a good example of an almost totally elastic collision, due to their high rigidity , but when bodies come in contact there is always some dissipation . A head-on elastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are v A1 and v B1 before the collision and v A2 and v B2 after,

1350-603: Is a measurable quantity, and the measurement depends on the frame of reference . For example: if an aircraft of mass 1000 kg is flying through the air at a speed of 50 m/s its momentum can be calculated to be 50,000 kg.m/s. If the aircraft is flying into a headwind of 5 m/s its speed relative to the surface of the Earth is only 45 m/s and its momentum can be calculated to be 45,000 kg.m/s. Both calculations are equally correct. In both frames of reference, any change in momentum will be found to be consistent with

1440-402: Is about 20 mph. This ability reflects the ability of the human shoulder muscles and tendons to store elasticity until it is needed to propel an object. A sling is a projectile weapon typically used to throw a blunt projectile such as a stone, clay or lead " sling-bullet ". A sling has a small cradle or pouch in the middle of two lengths of cord. The sling stone is placed in

1530-466: Is an inelastic collision . An elastic collision is one in which no kinetic energy is transformed into heat or some other form of energy. Perfectly elastic collisions can occur when the objects do not touch each other, as for example in atomic or nuclear scattering where electric repulsion keeps the objects apart. A slingshot maneuver of a satellite around a planet can also be viewed as a perfectly elastic collision. A collision between two pool balls

1620-605: Is equal to the instantaneous force F acting on it, F = d p d t . {\displaystyle F={\frac {{\text{d}}p}{{\text{d}}t}}.} If the net force experienced by a particle changes as a function of time, F ( t ) , the change in momentum (or impulse J ) between times t 1 and t 2 is Δ p = J = ∫ t 1 t 2 F ( t ) d t . {\displaystyle \Delta p=J=\int _{t_{1}}^{t_{2}}F(t)\,{\text{d}}t\,.} Impulse

1710-407: Is known as Euler's first law . If the net force F applied to a particle is constant, and is applied for a time interval Δ t , the momentum of the particle changes by an amount Δ p = F Δ t . {\displaystyle \Delta p=F\Delta t\,.} In differential form, this is Newton's second law ; the rate of change of the momentum of a particle

1800-468: Is measured in the derived units of the newton second (1 N⋅s = 1 kg⋅m/s) or dyne second (1 dyne⋅s = 1 g⋅cm/s) Under the assumption of constant mass m , it is equivalent to write F = d ( m v ) d t = m d v d t = m a , {\displaystyle F={\frac {{\text{d}}(mv)}{{\text{d}}t}}=m{\frac {{\text{d}}v}{{\text{d}}t}}=ma,} hence

1890-560: Is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics , quantum mechanics , quantum field theory , and general relativity . It is an expression of one of the fundamental symmetries of space and time: translational symmetry . Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics , allow one to choose coordinate systems that incorporate symmetries and constraints. In these systems

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1980-466: Is numerically equivalent to 3 newtons. In a closed system (one that does not exchange any matter with its surroundings and is not acted on by external forces) the total momentum remains constant. This fact, known as the law of conservation of momentum , is implied by Newton's laws of motion . Suppose, for example, that two particles interact. As explained by the third law, the forces between them are equal in magnitude but opposite in direction. If

2070-422: Is the center of mass frame – one that is moving with the center of mass. In this frame, the total momentum is zero. If two particles, each of known momentum, collide and coalesce, the law of conservation of momentum can be used to determine the momentum of the coalesced body. If the outcome of the collision is that the two particles separate, the law is not sufficient to determine the momentum of each particle. If

2160-499: Is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then the object's momentum p (from Latin pellere "push, drive") is: p = m v . {\displaystyle \mathbf {p} =m\mathbf {v} .} In the International System of Units (SI),

2250-401: Is the launching of a projectile by hand. Although some other animals can throw, humans are unusually good throwers due to their high dexterity and good timing capabilities, and it is believed that this is an evolved trait. Evidence of human throwing dates back 2 million years. The 90 mph throwing speed found in many athletes far exceeds the speed at which chimpanzees can throw things, which

2340-409: Is the product of the units of mass and velocity. In SI units , if the mass is in kilograms and the velocity is in meters per second then the momentum is in kilogram meters per second (kg⋅m/s). In cgs units , if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters per second (g⋅cm/s). Being a vector, momentum has magnitude and direction. For example,

2430-440: Is the study of the behavior and effects of a projectile when it hits its target. Terminal ballistics is relevant both for small caliber projectiles as well as for large caliber projectiles (fired from artillery ). The study of extremely high velocity impacts is still very new and is as yet mostly applied to spacecraft design. Forensic ballistics involves analysis of bullets and bullet impacts to determine information of use to

2520-499: Is the trafficking of contraband weapons and ammunition . What constitutes legal trade in firearms varies widely, depending on local and national laws. In 2001, the United Nations had made a protocol against the manufacturing and trafficking of illicit arms. This protocol made governments dispose illegal arms, and to licence new firearms being produced, to ensure them being legitimate. It was signed by 122 parties. There are

2610-455: Is unchanged. Forces such as Newtonian gravity, which depend only on the scalar distance between objects, satisfy this criterion. This independence of reference frame is called Newtonian relativity or Galilean invariance . A change of reference frame, can, often, simplify calculations of motion. For example, in a collision of two particles, a reference frame can be chosen, where, one particle begins at rest. Another, commonly used reference frame,

2700-459: The Franck–Hertz experiment ); and particle accelerators in which the kinetic energy is converted into mass in the form of new particles. In a perfectly inelastic collision (such as a bug hitting a windshield), both bodies have the same motion afterwards. A head-on inelastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If

2790-467: The Geneva Protocol , was issued in 1925 and was accepted as policy by all major countries. In 1937, poison gas was manufactured in large quantities but not used except against nations that lacked modern weapons or gas masks. Many modern military weapons, particularly ground-based ones, are relatively minor improvements to weapon systems developed during World War II. World War II marked perhaps

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2880-548: The Schöningen spears , eight wooden throwing spears dating back more than 300,000 years. At the site of Nataruk in Turkana, Kenya, numerous human skeletons dating to 10,000 years ago may present evidence of traumatic injuries to the head, neck, ribs, knees, and hands, including obsidian projectiles embedded in the bones that might have been caused by arrows and clubs during conflict between two hunter-gatherer groups. But

2970-426: The ancient Greeks . A gun is a normally tubular weapon or other device designed to discharge projectiles or other material. The projectile may be solid, liquid, gas, or energy and may be free, as with bullets and artillery shells, or captive as with Taser probes and whaling harpoons . The means of projection varies according to design but is usually effected by the action of gas pressure, either produced through

3060-580: The arquebus were much more powerful than human-powered weapons. Firearms became increasingly important and effective during the 16th–19th centuries, with progressive improvements in ignition mechanisms followed by revolutionary changes in ammunition handling and propellant. During the American Civil War , new applications of firearms, including the machine gun and ironclad warship , emerged that would still be recognizable and useful military weapons today, particularly in limited conflicts . In

3150-585: The trireme , were in use by the 7th century BC. During the first First Punic War , the use of advanced warships contributed to a Roman victory over the Carthaginians. European warfare during post-classical history was dominated by elite groups of knights supported by massed infantry (both in combat and ranged roles). They were involved in mobile combat and sieges , which involved various siege weapons and tactics. Knights on horseback developed tactics for charging with lances , providing an impact on

3240-405: The unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is dimensionally equivalent to the newton-second . Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference , but in any inertial frame it is a conserved quantity, meaning that if a closed system

3330-480: The 12th century the technology was spreading through the rest of Asia, and into Europe by the 13th century. After millennia of empirical development, the discipline of ballistics was initially studied and developed by Italian mathematician Niccolò Tartaglia in 1531, although he continued to use segments of straight-line motion, conventions established by the Greek philosopher Aristotle and Albert of Saxony , but with

3420-409: The 19th century, warship propulsion changed from sail power to fossil fuel -powered steam engines . Since the mid-18th century North American French-Indian war through the beginning of the 20th century, human-powered weapons were reduced from the primary weaponry of the battlefield to yielding gunpowder-based weaponry. Sometimes referred to as the "Age of Rifles", this period was characterized by

3510-569: The 4th century BC. Cavalry developed once horses were bred to support the weight of a human. The horse extended the range and increased the speed of attacks. Alexander's conquest saw the increased use of spears and shields in the Middle East and Western Asia as a result Greek culture spread which saw many Greek and other European weapons be used in these regions and as a result many of these weapons were adapted to fit their new use in war In addition to land-based weaponry, warships , such as

3600-581: The aid of explosive devices – particularly various types of ancient and medieval siege engines . The catapult has been used since ancient times, because it was proven to be one of the most effective mechanisms during warfare. The word "catapult" comes from the Latin catapulta , which in turn comes from the Greek καταπέλτης ( katapeltēs ), itself from κατά ( kata ), "against” and πάλλω ( pallō ), "to toss, to hurl". Catapults were invented by

3690-622: The atmosphere and work very well in space. Rockets for military and recreational uses date back to at least 13th century China . Significant scientific, interplanetary and industrial use did not occur until the 20th century, when rocketry was the enabling technology for the Space Age , including setting foot on the Moon . Rockets are now used for fireworks , weaponry , ejection seats , launch vehicles for artificial satellites , human spaceflight , and space exploration . Chemical rockets are

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3780-442: The beginning of the implementation of firearms in western warfare. Guns and rockets were introduced to the battlefield. Firearms are qualitatively different from earlier weapons because they release energy from combustible propellants , such as gunpowder , rather than from a counterweight or spring. This energy is released very rapidly and can be replicated without much effort by the user. Therefore, even early firearms such as

3870-469: The behaviour of a non-powered projectile in flight. External ballistics is frequently associated with firearms , and deals with the unpowered free-flight phase of the bullet after it exits the gun barrel and before it hits the target, so it lies between transitional ballistics and terminal ballistics . However, external ballistics is also concerned with the free-flight of rockets and other projectiles, such as balls, arrows etc. Terminal ballistics

3960-502: The conserved quantity is generalized momentum , and in general this is different from the kinetic momentum defined above. The concept of generalized momentum is carried over into quantum mechanics, where it becomes an operator on a wave function . The momentum and position operators are related by the Heisenberg uncertainty principle . In continuous systems such as electromagnetic fields , fluid dynamics and deformable bodies ,

4050-498: The development of ancient weapons. It was not the introduction of early Iron Age swords , however, as they were not superior to their bronze predecessors, but rather the domestication of the horse and widespread use of spoked wheels by c.  2000 BC . This led to the creation of the light, horse-drawn chariot , whose improved mobility proved important during this era. Spoke-wheeled chariot usage peaked around 1300 BC and then declined, ceasing to be militarily relevant by

4140-426: The development of firearms for infantry and cannons for support, as well as the beginnings of mechanized weapons such as the machine gun . Artillery pieces such as howitzers were able to destroy masonry fortresses and other fortifications, and this single invention caused a revolution in military affairs , establishing tactics and doctrine that are still in use today. An important feature of industrial age warfare

4230-428: The development, production, stockpiling, proliferation, and usage of weapons, from small arms and heavy weapons to weapons of mass destruction . Arms control is typically exercised through the use of diplomacy, which seeks to impose such limitations upon consenting participants, although it may also comprise efforts by a nation or group of nations to enforce limitations upon a non-consenting country. Arms trafficking

4320-468: The efficacy and efficiency of activities such as hunting , crime (e.g., murder ), law enforcement , self-defense , warfare , or suicide . In a broader context, weapons may be construed to include anything used to gain a tactical, strategic, material, or mental advantage over an adversary or enemy target. While ordinary objects such as sticks , rocks , bottles , chairs , and vehicles can be used as weapons , many objects are expressly designed for

4410-409: The end of this period revolutionized warfare. Formations of musketeers , protected by pikemen , came to dominate open battles, and the cannon replaced the trebuchet as the dominant siege weapon . The Ottoman used the cannon to destroy much of the fortifications at Constantinople which would change warfare as gunpowder became more available and technology improved The European Renaissance marked

4500-652: The enemy formations, and then drawing more practical weapons (such as swords ) once they entered melee. By contrast, infantry, in the age before structured formations, relied on cheap, sturdy weapons such as spears and billhooks in close combat and bows from a distance. As armies became more professional, their equipment was standardized, and infantry transitioned to pikes . Pikes are normally seven to eight feet in length and used in conjunction with smaller sidearms (short swords). In Eastern and Middle Eastern warfare, similar tactics were developed independent of European influences. The introduction of gunpowder from Asia at

4590-914: The equations expressing conservation of momentum and kinetic energy are: m A v A 1 + m B v B 1 = m A v A 2 + m B v B 2 1 2 m A v A 1 2 + 1 2 m B v B 1 2 = 1 2 m A v A 2 2 + 1 2 m B v B 2 2 . {\displaystyle {\begin{aligned}m_{A}v_{A1}+m_{B}v_{B1}&=m_{A}v_{A2}+m_{B}v_{B2}\\{\tfrac {1}{2}}m_{A}v_{A1}^{2}+{\tfrac {1}{2}}m_{B}v_{B1}^{2}&={\tfrac {1}{2}}m_{A}v_{A2}^{2}+{\tfrac {1}{2}}m_{B}v_{B2}^{2}\,.\end{aligned}}} A change of reference frame can simplify analysis of

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4680-423: The first lethal projectile ever described in discussion of ballistics. A string joins the two ends and when the string is drawn back, the ends of the stick are flexed. When the string is released, the potential energy of the flexed stick is transformed into the velocity of the arrow. Archery is the art or sport of shooting arrows from bows. A catapult is a device used to launch a projectile a great distance without

4770-605: The first time made it possible to successfully predict trajectories. The word ballistics comes from the Greek βάλλειν ballein , meaning "to throw". A projectile is any object projected into space (empty or not) by the exertion of a force . Although any object in motion through space (for example a thrown baseball ) is a projectile, the term most commonly refers to a ranged weapon . Mathematical equations of motion are used to analyze projectile trajectory . Examples of projectiles include balls , arrows , bullets , artillery shells , wingless rockets , etc. Throwing

4860-765: The following: p = ∑ i m i v i . {\displaystyle p=\sum _{i}m_{i}v_{i}.} A system of particles has a center of mass , a point determined by the weighted sum of their positions: r cm = m 1 r 1 + m 2 r 2 + ⋯ m 1 + m 2 + ⋯ = ∑ i m i r i ∑ i m i . {\displaystyle r_{\text{cm}}={\frac {m_{1}r_{1}+m_{2}r_{2}+\cdots }{m_{1}+m_{2}+\cdots }}={\frac {\sum _{i}m_{i}r_{i}}{\sum _{i}m_{i}}}.} If one or more of

4950-456: The force is between particles. Similarly, if there are several particles, the momentum exchanged between each pair of particles adds to zero, so the total change in momentum is zero. The conservation of the total momentum of a number of interacting particles can be expressed as m A v A + m B v B + m C v C + . . . = c o n s t

5040-1047: The initial velocities are known, the final velocities are given by v A 2 = ( m A − m B m A + m B ) v A 1 + ( 2 m B m A + m B ) v B 1 v B 2 = ( m B − m A m A + m B ) v B 1 + ( 2 m A m A + m B ) v A 1 . {\displaystyle {\begin{aligned}v_{A2}&=\left({\frac {m_{A}-m_{B}}{m_{A}+m_{B}}}\right)v_{A1}+\left({\frac {2m_{B}}{m_{A}+m_{B}}}\right)v_{B1}\\v_{B2}&=\left({\frac {m_{B}-m_{A}}{m_{A}+m_{B}}}\right)v_{B1}+\left({\frac {2m_{A}}{m_{A}+m_{B}}}\right)v_{A1}\,.\end{aligned}}} If one body has much greater mass than

5130-437: The innovation that he connected the straight lines by a circular arc. Galileo established the principle of compound motion in 1638, using the principle to derive the parabolic form of the ballistic trajectory. Ballistics was put on a solid scientific and mathematical basis by Isaac Newton , with the publication of Philosophiæ Naturalis Principia Mathematica in 1687. This gave mathematical laws of motion and gravity which for

5220-470: The interpretation of warfare at Nataruk has been challenged due to conflicting evidence. The earliest ancient weapons were evolutionary improvements of late Neolithic implements, but significant improvements in materials and crafting techniques led to a series of revolutions in military technology . The development of metal tools began with copper during the Copper Age (about 3,300 BC) and

5310-476: The interwar period (between WWI and WWII) with the continuous evolution of weapon systems by all major industrial powers. The major armament firms were Schneider-Creusot (based in France), Škoda Works (Czechoslovakia), and Vickers (Great Britain). The 1920s were committed to disarmament and the outlawing of war and poison gas, but rearmament picked up rapidly in the 1930s. The munitions makers responded nimbly to

5400-535: The laws of classical mechanics ; in contrast to (for example) a cruise missile which is aerodynamically guided in powered flight like a fixed-wing aircraft . The earliest known ballistic projectiles were stones and spears, and the throwing stick . The oldest evidence of stone-tipped projectiles, which may or may not have been propelled by a bow (c.f. atlatl ), dating to c. 280,000 years ago, were found in Ethiopia, present day-East-Africa. The oldest evidence of

5490-572: The manufacture, sale, transfer, possession, modification, and use of small arms by civilians. Countries that regulate access to firearms will typically restrict access to certain categories of firearms and then restrict the categories of persons who may be granted a license for access to such firearms. There may be separate licenses for hunting, sport shooting (a.k.a. target shooting), self-defense, collecting, and concealed carry, with different sets of requirements, permissions, and responsibilities. International treaties and agreements place restrictions on

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5580-411: The momentum of one particle after the collision is known, the law can be used to determine the momentum of the other particle. Alternatively if the combined kinetic energy after the collision is known, the law can be used to determine the momentum of each particle after the collision. Kinetic energy is usually not conserved. If it is conserved, the collision is called an elastic collision ; if not, it

5670-424: The most common type of high performance rocket and they typically create their exhaust by the combustion of rocket propellant . Chemical rockets store a large amount of energy in an easily released form, and can be very dangerous. However, careful design, testing, construction and use minimizes risks. Ballistics is often broken down into the following four categories: Internal ballistics (also interior ballistics),

5760-453: The most frantic period of weapon development in the history of humanity. Massive numbers of new designs and concepts were fielded, and all existing technologies were improved between 1939 and 1945. The most powerful weapon invented during this period was the nuclear bomb ; however, many other weapons influenced the world, such as jet aircraft and radar , but were overshadowed by the visibility of nuclear weapons and long-range rockets. Since

5850-402: The motion of rockets and other spacecraft . The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation . It is a core discipline within space mission design and control. Momentum In Newtonian mechanics , momentum ( pl. : momenta or momentums ; more specifically linear momentum or translational momentum )

5940-742: The negative sign indicating that the forces oppose. Equivalently, d d t ( p 1 + p 2 ) = 0. {\displaystyle {\frac {\text{d}}{{\text{d}}t}}\left(p_{1}+p_{2}\right)=0.} If the velocities of the particles are v A1 and v B1 before the interaction, and afterwards they are v A2 and v B2 , then m A v A 1 + m B v B 1 = m A v A 2 + m B v B 2 . {\displaystyle m_{A}v_{A1}+m_{B}v_{B1}=m_{A}v_{A2}+m_{B}v_{B2}.} This law holds no matter how complicated

6030-400: The net force is equal to the mass of the particle times its acceleration . Example : A model airplane of mass 1 kg accelerates from rest to a velocity of 6 m/s due north in 2 s. The net force required to produce this acceleration is 3  newtons due north. The change in momentum is 6 kg⋅m/s due north. The rate of change of momentum is 3 (kg⋅m/s)/s due north which

6120-447: The other, its velocity will be little affected by a collision while the other body will experience a large change. In an inelastic collision, some of the kinetic energy of the colliding bodies is converted into other forms of energy (such as heat or sound ). Examples include traffic collisions , in which the effect of loss of kinetic energy can be seen in the damage to the vehicles; electrons losing some of their energy to atoms (as in

6210-456: The particles are numbered 1 and 2, the second law states that F 1 = ⁠ d p 1 / d t ⁠ and F 2 = ⁠ d p 2 / d t ⁠ . Therefore, d p 1 d t = − d p 2 d t , {\displaystyle {\frac {{\text{d}}p_{1}}{{\text{d}}t}}=-{\frac {{\text{d}}p_{2}}{{\text{d}}t}},} with

6300-421: The particles is moving, the center of mass of the system will generally be moving as well (unless the system is in pure rotation around it). If the total mass of the particles is m {\displaystyle m} , and the center of mass is moving at velocity v cm , the momentum of the system is: p = m v cm . {\displaystyle p=mv_{\text{cm}}.} This

6390-405: The period during which a rocket engine is providing thrust. Transitional ballistics, also known as intermediate ballistics, is the study of a projectile's behavior from the time it leaves the muzzle until the pressure behind the projectile is equalized, so it lies between internal ballistics and external ballistics . External ballistics is the part of the science of ballistics that deals with

6480-413: The point of being able to ensure the destruction of the Earth by 100 fold, a new tactic had to be developed. With this realization, armaments development funding shifted back to primarily sponsoring the development of conventional arms technologies for support of limited wars rather than total war . The arms industry is a global industry that involves the sale and manufacture of weaponry. It consists of

6570-404: The pouch. The middle finger or thumb is placed through a loop on the end of one cord, and a tab at the end of the other cord is placed between the thumb and forefinger. The sling is swung in an arc, and the tab released at a precise moment. This frees the projectile to fly to the target. A bow is a flexible piece of material which shoots aerodynamic projectiles called arrows . The arrow is perhaps

6660-412: The purpose; these range from simple implements such as clubs , axes , spears , and swords to complicated modern firearms , tanks , intercontinental ballistic missiles , biological weapons , and cyberweapons . Something that has been repurposed, converted, or enhanced to become a weapon of war is termed weaponized , such as a weaponized virus or weaponized laser . The use of weapons has been

6750-476: The rapid combustion of a propellant or compressed and stored by mechanical means, operating on the projectile inside an open-ended tube in the fashion of a piston. The confined gas accelerates the movable projectile down the length of the tube imparting sufficient velocity to sustain the projectile's travel once the action of the gas ceases at the end of the tube or muzzle. Alternatively, acceleration via electromagnetic field generation may be employed in which case

6840-529: The rapidly shifting strategic and economic landscape. The main purchasers of munitions from the big three companies were Romania, Yugoslavia, Greece, and Turkey – and, to a lesser extent, Poland, Finland, the Baltic States, and the Soviet Union. Realistic critics understood that war could not really be outlawed, but its worst excesses might be banned. Poison gas became the focus of

6930-553: The realization of mutual assured destruction (MAD), the nuclear option of all-out war is no longer considered a survivable scenario. During the Cold War in the years following World War II, both the United States and the Soviet Union engaged in a nuclear arms race . Each country and their allies continually attempted to out-develop each other in the field of nuclear armaments. Once the joint technological capabilities reached

7020-613: The realms of known physical possibility. At its most prosaic, science fiction features an endless variety of sidearms , mostly variations on real weapons such as guns and swords . Among the best-known of these are the phaser used in the Star Trek television series, films, and novels, and the lightsaber and blaster featured in the Star Wars movies, comics, novels, and TV series. In addition to adding action and entertainment value, weaponry in science fiction sometimes becomes

7110-402: The relevant laws of physics. Suppose x is a position in an inertial frame of reference. From the point of view of another frame of reference, moving at a constant speed u relative to the other, the position (represented by a primed coordinate) changes with time as x ′ = x − u t . {\displaystyle x'=x-ut\,.} This is called

7200-538: The resulting direction and speed of motion of objects after they collide. Below, the basic properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations (see multiple dimensions ). The momentum of a particle is conventionally represented by the letter p . It is the product of two quantities, the particle's mass (represented by the letter m ) and its velocity ( v ): p = m v . {\displaystyle p=mv.} The unit of momentum

7290-403: The rocket before use. Rocket engines work by action and reaction . Rocket engines push rockets forward simply by throwing their exhaust backwards extremely fast. While comparatively inefficient for low speed use, rockets are relatively lightweight and powerful, capable of generating large accelerations and of attaining extremely high speeds with reasonable efficiency. Rockets are not reliant on

7380-644: The same speed. Adding the speed of the center of mass to both, we find that the body that was moving is now stopped and the other is moving away at speed v . The bodies have exchanged their velocities. Regardless of the velocities of the bodies, a switch to the center of mass frame leads us to the same conclusion. Therefore, the final velocities are given by v A 2 = v B 1 v B 2 = v A 1 . {\displaystyle {\begin{aligned}v_{A2}&=v_{B1}\\v_{B2}&=v_{A1}\,.\end{aligned}}} In general, when

7470-418: The second reference frame is also an inertial frame and the accelerations are the same: a ′ = d v ′ d t = a . {\displaystyle a'={\frac {{\text{d}}v'}{{\text{d}}t}}=a\,.} Thus, momentum is conserved in both reference frames. Moreover, as long as the force has the same form, in both frames, Newton's second law

7560-402: The tube may be dispensed with and a guide rail substituted. A weapons engineer or armourer who applies the scientific principles of ballistics to design cartridges are often called a ballistician . A rocket is a missile , spacecraft , aircraft or other vehicle that obtains thrust from a rocket engine . Rocket engine exhaust is formed entirely from propellants carried within

7650-850: The use of bows to shoot arrows dates to about 10,000 years ago; it is based on pinewood arrows found in the Ahrensburg valley north of Hamburg . They had shallow grooves on the base, indicating that they were shot from a bow. The oldest bow so far recovered is about 8,000 years old, found in the Holmegård swamp in Denmark. Archery seems to have arrived in the Americas with the Arctic small tool tradition , about 4,500 years ago. The first devices identified as guns appeared in China around 1000 AD, and by

7740-419: The velocities are v A1 and v B1 before the collision then in a perfectly inelastic collision both bodies will be travelling with velocity v 2 after the collision. The equation expressing conservation of momentum is: Weapon A weapon , arm , or armament is any implement or device that is used to deter, threaten, inflict physical damage, harm, or kill . Weapons are used to increase

7830-461: The wide introduction of aircraft into warfare and naval warfare with the introduction of aircraft carriers . Above all, it promised the military commanders independence from horses and a resurgence in maneuver warfare through the extensive use of motor vehicles. The changes that these military technologies underwent were evolutionary but defined their development for the rest of the century. This period of innovation in weapon design continued in

7920-410: Was technological escalation – innovations were rapidly matched through replication or countered by another innovation. World War I marked the entry of fully industrialized warfare as well as weapons of mass destruction ( e.g. , chemical and biological weapons ), and new weapons were developed quickly to meet wartime needs. The technological escalation during World War I was profound, including

8010-434: Was 16 percent higher than in 2005–2009, and the arms sales of the world's 100 largest private arms-producing and military services companies totaled $ 420 billion in 2018. The production, possession, trade, and use of many weapons are controlled. This may be at a local or central government level or by international treaty. Examples of such controls include: All countries have laws and policies regulating aspects such as

8100-632: Was followed by the Bronze Age , leading to the creation of the Bronze Age sword and similar weapons. During the Bronze Age, the first defensive structures and fortifications appeared as well, indicating an increased need for security. Weapons designed to breach fortifications followed soon after, such as the battering ram , which was in use by 2500 BC. The development of ironworking around 1300 BC in Greece had an important impact on

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