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# CONSERVATION LAWS

## CONCEPT

The term "conservation laws" might sound at first like a body of legal statutes geared toward protecting the environment. In physics, however, the term refers to a set of principles describing certain aspects of the physical universe that are preserved throughout any number of reactions and interactions. Among the properties conserved are energy, linear momentum, angular momentum, and electrical charge. (Mass, too, is conserved, though only in situations well below the speed of light.) The conservation of these properties can be illustrated by examples as diverse as dropping a ball (energy); the motion of a skater spinning on ice (angular momentum); and the recoil of a rifle (linear momentum).

## HOW IT WORKS

The conservation laws describe physical properties that remain constant throughout the various processes that occur in the physical world. In physics, "to conserve" something means "to result in no net loss of" that particular component. For each such component, the input is the same as the output: if one puts a certain amount of energy into a physical system, the energy that results from that system will be the same as the energy put into it.

The energy may, however, change forms. In addition, the operations of the conservation laws areon Earth, at leastusually affected by a number of other forces, such as gravity, friction, and air resistance. The effects of these forces, combined with the changes in form that take place within a given conserved property, sometimes make it difficult to perceive the working of the conservation laws. It was stated above that the resulting energy of a physical system will be the same as the energy that was introduced to it. Note, however, that the usable energy output of a system will not be equal to the energy input. This is simply impossible, due to the factors mentioned aboveparticularly friction.

When one puts gasoline into a motor, for instance, the energy that the motor puts out will never be as great as the energy contained in the gasoline, because part of the input energy is expended in the operation of the motor itself. Similarly, the angular momentum of a skater on ice will ultimately be dissipated by the resistant force of friction, just as that of a Frisbee thrown through the air is opposed both by gravity and air resistanceitself a specific form of friction.

In each of these cases, however, the property is still conserved, even if it does not seem so to the unaided senses of the observer. Because the motor has a usable energy output less than the input, it seems as though energy has been lost. In fact, however, the energy has only changed forms, and some of it has been diverted to areas other than the desired output. (Both the noise and the heat of the motor, for instance, represent uses of energy that are typically considered undesirable.) Thus, upon closer study of the motoritself an example of a systemit becomes clear that the resulting energy, if not the desired usable output, is the same as the energy input.

As for the angular momentum examples in which friction, or air resistance, plays a part, here too (despite all apparent evidence to the contrary) the property is conserved. This is easier to understand if one imagines an object spinning in outer space, free from the opposing force of friction. Thanks to the conservation of angular momentum, an object set into rotation in space will continue to spin indefinitely. Thus, if an astronaut in the 1960s, on a spacewalk from his capsule, had set a screwdriver spinning in the emptiness of the exosphere, the screwdriver would still be spinning today!

### Energy and Mass

Among the most fundamental statements in all of science is the conservation of energy: a system isolated from all outside factors will maintain the same total amount of energy, even though energy transformations from one form or another take place.

Energy is manifested in many varieties, including thermal, electromagnetic, sound, chemical, and nuclear energy, but all these are merely reflections of three basic types of energy. There is potential energy, which an object possesses by virtue of its position; kinetic energy, which it possesses by virtue of its motion; and rest energy, which it possesses by virtue of its mass.

The last of these three will be discussed in the context of the relationship between energy and mass; at present the concern is with potential and kinetic energy. Every system possesses a certain quantity of both, and the sum of its potential and kinetic energy is known as mechanical energy. The mechanical energy within a system does not change, but the relative values of potential and kinetic energy may be altered.

#### A SIMPLE EXAMPLE OF MECHANICAL ENERGY.

If one held a baseball at the top of a tall building, it would have a certain amount of potential energy. Once it was dropped, it would immediately begin losing potential energy and gaining kinetic energy proportional to the potential energy it lost. The relationship between the two forms, in fact, is inverse: as the value of one variable decreases, that of the other increases in exact proportion.

The ball cannot keep falling forever, losing potential energy and gaining kinetic energy. In fact, it can never gain an amount of kinetic energy greater than the potential energy it possessed in the first place. At the moment before it hits the ground, the ball's kinetic energy is equal to the potential energy it possessed at the top of the building. Correspondingly, its potential energy is zerothe same amount of kinetic energy it possessed before it was dropped.

Then, as the ball hits the ground, the energy is dispersed. Most of it goes into the ground, and depending on the rigidity of the ball and the ground, this energy may cause the ball to bounce. Some of the energy may appear in the form of sound, produced as the ball hits bottom, and some will manifest as heat. The total energy, however, will not be lost: it will simply have changed form.

#### REST ENERGY.

The values for mechanical energy in the above illustration would most likely be very small; on the other hand, the rest or mass energy of the baseball would be staggering. Given the weight of 0.333 pounds for a regulation baseball, which on Earth converts to 0.15 kg in mass, it would possess enough energy by virtue of its mass to provide a year's worth of electrical power to more than 150,000 American homes. This leads to two obvious questions: how can a mere baseball possess all that energy? And if it does, how can the energy be extracted and put to use?

The answer to the second question is, "By accelerating it to something close to the speed of light"which is more than 27,000 times faster than the fastest speed ever achieved by humans. (The astronauts on Apollo 10 in May 1969 reached nearly 25,000 MPH (40,000 km/h), which is more than 33 times the speed of sound but still insignificant when compared to the speed of light.) The answer to the first question lies in the most well-known physics formula of all time: E = mc 2

In 1905, Albert Einstein (1879-1955) published his Special Theory of Relativity, which he followed a decade later with his General Theory of Relativity. These works introduced the world to the above-mentioned formula, which holds that energy is equal to mass multiplied by the squared speed of light. This formula gained its widespread prominence due to the many implications of Einstein's Relativity, which quite literally changed humanity's perspective on the universe. Most concrete among those implications was the atom bomb, made possible by the understanding of mass and energy achieved by Einstein.

In fact, E = mc 2 is the formula for rest energy, sometimes called mass energy. Though rest energy is "outside" of kinetic and potential energy in the sense that it is not defined by the above-described interactions within the larger system of mechanical energy, its relation to the other forms can be easily shown. All three are defined in terms of mass. Potential energy is equal to mgh, where m is mass, g is gravity, and h is height. Kinetic energy is equal to ½ mv 2, where v is velocity. In factusing a series of steps that will not be demonstrated hereit is possible to directly relate the kinetic and rest energy formulae.

The kinetic energy formula describes the behavior of objects at speeds well below the speed of light, which is 186,000 mi (297,600 km) per second. But at speeds close to that of the speed of light, ½ mv 2 does not accurately reflect the energy possessed by the object. For instance, if v were equal to 0.999 c (where c represents the speed of light), then the application of the formula ½ mv 2 would yield a value equal to less than 3% of the object's real energy. In order to calculate the true energy of an object at 0.999 c, it would be necessary to apply a different formula for total energy, one that takes into account the fact that, at such a speed, mass itself becomes energy.

#### CONSERVATION OF MASS.

Mass itself is relative at speeds approaching c, and, in fact, becomes greater and greater the closer an object comes to the speed of light. This may seem strange in light of the fact that there is, after all, a law stating that mass is conserved. But mass is only conserved at speeds well below c: as an object approaches 186,000 mi (297,600 km) per second, the rules are altered.

The conservation of mass states that total mass is constant, and is unaffected by factors such as position, velocity, or temperature, in any system that does not exchange any matter with its environment. Yet, at speeds close to c, the mass of an object increases dramatically.

In such a situation, the mass would be equal to the rest, or starting mass, of the object divided by (1 (v 2/c 2), where v is the object's speed of relative motion. The denominator of this equation will always be less than one, and the greater the value of v, the smaller the value of the denominator. This means that at a speed of c, the denominator is zeroin other words, the object's mass is infinite! Obviously, this is not possible, and indeed, what the formula actually shows is that no object can travel faster than the speed of light.

Of particular interest to the present discussion, however, is the fact, established by relativity theory, that mass can be converted into energy. Hence, as noted earlier, a baseball or indeed any object can be converted into energyand since the formula for rest energy requires that the mass be multiplied by c 2, clearly, even an object of virtually negligible mass can generate a staggering amount of energy. This conversion of mass to energy happens well below the speed of light, in a very small way, when a stick of dynamite explodes. A portion of that stick becomes energy, and the fact that this portion is equal to just 6 parts out of 100 billion indicates the vast proportions of energy available from converted mass.

### Other Conservation Laws

In addition to the conservation of energy, as well as the limited conservation of mass, there are laws governing the conservation of momentum, both for an object in linear (straight-line) motion, and for one in angular (rotational) motion. Momentum is a property that a moving body possesses by virtue of its mass and velocity, which determines the amount of force and time required to stop it. Linear momentum is equal to mass multiplied by velocity, and the conservation of linear momentum law states that when the sum of the external force vectors acting on a physical system is equal to zero, the total linear momentum of the system remains unchanged, or conserved.

Angular momentum, or the momentum of an object in rotational motion, is equal to mr 2ω, where m is mass, r is the radius of rotation, and ω (the Greek letter omega) stands for angular velocity. According to the conservation of angular momentum law, when the sum of the external torques acting on a physical system is equal to zero, the total angular momentum of the system remains unchanged. Torque is a force applied around an axis of rotation. When playing the old game of "spin the bottle," for instance, one is applying torque to the bottle and causing it to rotate.

#### ELECTRIC CHARGE.

The conservation of both linear and angular momentum are best explained in the context of real-life examples, provided below. Before going on to those examples, however, it is appropriate here to discuss a conservation law that is outside the realm of everyday experience: the conservation of electric charge, which holds that for an isolated system, the net electric charge is constant.

This law is "outside the realm of everyday experience" such that one cannot experience it through the senses, but at every moment, it is happening everywhere. Every atom has positively charged protons, negatively charged electrons, and uncharged neutrons. Most atoms are neutral, possessing equal numbers of protons and electrons; but, as a result of some disruption, an atom may have more protons than electrons, and thus, become positively charged. Conversely, it may end up with a net negative charge due to a greater number of electrons. But the protons or electrons it released or gained did not simply appear or disappear: they moved from one part of the system to anotherthat is, from one atom to another atom, or to several other atoms.

Throughout these changes, the charge of each proton and electron remains the same, and the net charge of the system is always the sum of its positive and negative charges. Thus, it is impossible for any electrical charge in the universe to be smaller than that of a proton or electron. Likewise, throughout the universe, there is always the same number of negative and positive electrical charges: just as energy changes form, the charges simply change position.

There are also conservation laws describing the behavior of subatomic particles, such as the positron and the neutrino. However, the most significant of the conservation laws are those involving energy (and mass, though with the limitations discussed above), linear momentum, angular momentum, and electrical charge.

## REAL-LIFE APPLICATIONS

### Conservation of Linear Momentum: Rifles and Rockets

#### FIRING A RIFLE.

The conservation of linear momentum is reflected in operations as simple as the recoil of a rifle when it is fired, and in those as complex as the propulsion of a rocket through space. In accordance with the conservation of momentum, the momentum of a system must be the same after it undergoes an operation as it was before the process began. Before firing, the momentum of a rifle and bullet is zero, and therefore, the rifle-bullet system must return to that same zero-level of momentum after it is fired. Thus, the momentum of the bullet must be matchedand "cancelled" within the system under studyby a corresponding backward momentum.

When a person shooting a gun pulls the trigger, it releases the bullet, which flies out of the barrel toward the target. The bullet has mass and velocity, and it clearly has momentum; but this is only half of the story. At the same time it is fired, the rifle produces a "kick," or sharp jolt, against the shoulder of the person who fired it. This backward kick, with a velocity in the opposite direction of the bullet's trajectory, has a momentum exactly the same as that of the bullet itself: hence, momentum is conserved.

But how can the rearward kick have the same momentum as that of the bullet? After all, the bullet can kill a person, whereas, if one holds the rifle correctly, the kick will not even cause any injury. The answer lies in several properties of linear momentum. First of all, as noted earlier, momentum is equal to mass multiplied by velocity; the actual proportions of mass and velocity, however, are not important as long as the backward momentum is the same as the forward momentum. The bullet is an object of relatively small mass and high velocity, whereas the rifle is much larger in mass, and hence, its rearward velocity is correspondingly small.

In addition, there is the element of impulse, or change in momentum. Impulse is the product of force multiplied by change or interval in time. Again, the proportions of force and time interval do not matter, as long as they are equal to the momentum changethat is, the difference in momentum that occurs when the rifle is fired. To avoid injury to one's shoulder, clearly force must be minimized, and for this to happen, time interval must be extended.

If one were to fire the rifle with the stock (the rear end of the rifle) held at some distance from one's shoulder, it would kick back and could very well produce a serious injury. This is because the force was delivered over a very short time intervalin other words, force was maximized and time interval minimized. However, if one holds the rifle stock firmly against one's shoulder, this slows down the delivery of the kick, thus maximizing time interval and minimizing force.

#### ROCKETING THROUGH SPACE.

Contrary to popular belief, rockets do not move by pushing against a surface such as a launchpad. If that were the case, then a rocket would have nothing to propel it once it had been launched, and certainly there would be no way for a rocket to move through the vacuum of outer space. Instead, what propels a rocket is the conservation of momentum.

Upon ignition, the rocket sends exhaust gases shooting downward at a high rate of velocity. The gases themselves have mass, and thus, they have momentum. To balance this downward momentum, the rocket moves upwardthough, because its mass is greater than that of the gases it expels, it will not move at a velocity as high as that of the gases. Once again, the upward or forward momentum is exactly the same as the downward or backward momentum, and linear momentum is conserved.

Rather than needing something to push against, a rocket in fact performs best in outer space, where there is nothingneither launch-pad nor even airagainst which to push. Not only is "pushing" irrelevant to the operation of the rocket, but the rocket moves much more efficiently without the presence of air resistance. In the same way, on the relatively frictionless surface of an ice-skating rink, conservation of linear momentum (and hence, the process that makes possible the flight of a rocket through space) is easy to demonstrate.

If, while standing on the ice, one throws an object in one direction, one will be pushed in the opposite direction with a corresponding level of momentum. However, since a person's mass is presumably greater than that of the object thrown, the rearward velocity (and, therefore, distance) will be smaller.

Friction, as noted earlier, is not the only force that counters conservation of linear momentum on Earth: so too does gravity, and thus, once again, a rocket operates much better in space than it does when under the influence of Earth's gravitational field. If a bullet is fired at a bottle thrown into the air, the linear momentum of the spent bullet and the shattered pieces of glass in the infinitesimal moment just after the collision will be the same as that of the bullet and the bottle a moment before impact. An instant later, however, gravity will accelerate the bullet and the pieces downward, thus leading to a change in total momentum.

### Conservation of Angular Momentum: Skaters and Other Spinners

As noted earlier, angular momentum is equal to mr 2ω, where m is mass, r is the radius of rotation, and ω stands for angular velocity. In fact, the first two quantities, mr 2, are together known as moment of inertia. For an object in rotation, moment of inertia is the property whereby objects further from the axis of rotation move faster, and thus, contribute a greater share to the overall kinetic energy of the body.

One of the most oft-cited examples of angular momentumand of its conservationinvolves a skater or ballet dancer executing a spin. As the skater begins the spin, she has one leg planted on the ice, with the other stretched behind her. Likewise, her arms are outstretched, thus creating a large moment of inertia. But when she goes into the spin, she draws in her arms and leg, reducing the moment of inertia. In accordance with conservation of angular momentum, mr 2ω will remain constant, and therefore, her angular velocity will increase, meaning that she will spin much faster.

#### CONSTANT ORIENTATION.

The motion of a spinning top and a Frisbee in flight also illustrate the conservation of angular momentum. Particularly interesting is the tendency of such an object to maintain a constant orientation. Thus, a top remains perfectly vertical while it spins, and only loses its orientation once friction from the floor dissipates its velocity and brings it to a stop. On a frictionless surface, however, it would remain spinningand therefore uprightforever.

A Frisbee thrown without spin does not provide much entertainment; it will simply fall to the ground like any other object. But if it is tossed with the proper spin, delivered from the wrist, conservation of angular momentum will keep it in a horizontal position as it flies through the air. Once again, the Frisbee will eventually be brought to ground by the forces of air resistance and gravity, but a Frisbee hurled through empty space would keep spinning for eternity.

"Conservation Laws: An Online Physics Textbook" (Web site). <http://www.lightandmatter.com/area1book2.html> (March 12, 2001).

"Conservation Laws: The Most Powerful Laws of Physics" (Web site). <http://webug.physics.uiuc.edu/courses/phys150/fall 99/slides/lect07/> (March 12, 2001).

"Conservation of Energy." NASA (Web site). <http://www.grc.nasa.gov/WWW/K-12/airplane/thermo1f.html> (March 12, 2001).

Elkana, Yehuda. The Discovery of the Conservation of Energy. With a foreword by I. Bernard Cohen. Cambridge, MA: Harvard University Press, 1974.

"Momentum and Its Conservation" (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/momtoc.html> (March 12, 2001).

Rutherford, F. James; Gerald Holton; and Fletcher G. Watson. Project Physics. New York: Holt, Rinehart, and Winston, 1981.

Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.

## KEY TERMS

### CONSERVATION LAWS:

A set of principles describing physical properties that remain constantthat is, are conservedthroughout the various processes that occur in the physical world. The most significant of these laws concerns the conservation of energy (as well as, with qualifications, the conservation of mass); conservation of linear momentum; conservation of angular momentum; and conservation of electrical charge.

### CONSERVATION OF ANGULAR MOMENTUM:

A physical law stating that when the sum of the external torques acting on a physical system is equal to zero, the total angular momentum of the system remains unchanged. Angular momentum is the momentum of an object in rotational motion, and torque is a force applied around an axis of rotation.

### CONSERVATION OF ELECTRICALCHARGE:

A physical law which holds that for an isolated system, the net electrical charge is constant.

### CONSERVATION OF ENERGY:

A law of physics stating that within a system isolated from all other outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place.

### CONSERVATION OF LINEAR MOMENTUM:

A physical law stating that when the sum of the external force vectorsacting on a physical system is equal to zero, the total linear momentum of the system remains unchangedor is conserved.

### CONSERVATION OF MASS:

A physical principle stating that total mass is constant, and is unaffected by factors such asposition, velocity, or temperature, in any system that does not exchange any matter with its environment. Unlike the other conservation laws, however, conservation of mass is not universally applicable, but applies only at speeds significant lower than that of light186,000 mi (297,600 km) per second. Close to the speed of light, mass begins converting to energy.

### CONSERVE:

In physics, "to conserve" something means "to result in no net loss of" that particular component. It is possible that within a given system, the component may change form or position, but as long as the net value of the component remains the same, it has been conserved.

### FRICTION:

The force that resists motion when the surface of one object comes into contact with the surface of another.

### MOMENTUM:

A property that a moving body possesses by virtue of its mass and velocity, which determines the amount of force and time required to stop it.

### SYSTEM:

In physics, the term "system" usually refers to any set of physical interactions isolated from the rest of the universe. Anything outside of the system, including all factors and forces irrelevant to a discussion of that system, is known as the environment.

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# Conservation laws

Conservation laws are scientific statements that describe the amount of some quantity before and after a physical or chemical change.

## Conservation of mass and energy

One of the first conservation laws to be discovered was the conservation of mass (or matter). Suppose that you combine a very accurately weighed amount of iron and sulfur with each other. The product of that reaction is a compound known as iron(II) sulfide. If you also weigh very accurately the amount of iron(II) sulfide formed in that reaction, you will discover a simple relationship: The weight of the beginning materials (iron plus sulfur) is exactly equal to the weight of the product or products of the reaction (iron(II) sulfide). This statement is one way to express the law of conservation of mass. A more formal definition of the law is that mass (or matter) cannot be created or destroyed in a chemical reaction.

A similar law exists for energy. When you turn on an electric heater, electrical energy is converted to heat energy. If you measure the amount of electricity supplied to the heater and the amount of heat produced by the heater, you will find the amounts are equal. In other words, energy is conserved in the heater. It may take various forms, such as electrical energy, heat, magnetism, or kinetic energy (the energy of an object due to its motion), but the relationship is always the same: The amount of energy used to initiate a change is the same as the amount of energy detected at the end of the change. In other words, energy cannot be created or destroyed in a physical or chemical change. This statement summarizes the law of conservation of energy.

## Words to Know

Angular momentum: For objects in rotational (or spinning) motion, the product of the object's mass, its speed, and its distance from the axis of rotation.

Conserved quantities: Physical quantities, the amounts of which remain constant before, during, and after some physical or chemical process.

Linear momentum: The product of an object's mass and its velocity.

Mass: A measure of the quantity of matter.

Subatomic particle: A particle smaller than an atom, such as a proton, neutron, or electron.

Velocity: The rate at which the position of an object changes with time, including both the speed and the direction.

At one time, scientists thought that the law of conservation of mass and the law of conservation of energy were two distinct laws. In the early part of the twentieth century, however, German-born American physicist Albert Einstein (18791955) demonstrated that matter and energy are two forms of the same thing. He showed that matter can change into energy and that energy can change into matter. Einstein's discovery required a restatement of the laws of conservation of mass and energy. In some instances, a tiny bit of matter can be created or destroyed in a change. The quantity is too small to be measured by ordinary balances, but it still amounts to something. Similarly, a small amount of energy can be created or destroyed in a change. But, the total amount of matter PLUS energy before and after a change still remains constant. This statement is now accepted as the law of conservation of mass and energy.

Examples of the law of conservation of mass and energy are common in everyday life. The manufacturer of an electric heater can tell consumers how much heat will be produced by a given model of heater. The amount of heat produced is determined by the amount of electrical current that goes into the heater. Similarly, the amount of gasoline that can be formed in the breakdown of petroleum can be calculated by the amount of petroleum used in the process. And the amount of nuclear energy produced by a nuclear power plant can be calculated by the amount of uranium-235 used in the plant.

Calculations such as these are never quite as simple as they sound. We think of an electric lightbulb, for example, as a way of changing electrical energy into light. Yet, more than 90 percent of that electricity is actually converted to heat. (Baby chicks are kept warm by the heat of lightbulbs.) Still, the conservation law holds true. The total amount of energy produced in a lightbulb (heat plus light) is equal to the total amount of energy put into the bulb in the form of electricity.

## Other conservation laws

Conservation of electric charge. Most physical properties abide by conservation laws. Electric charge is another example. Electric charge is the property that makes you experience a shock or spark when you touch a metal doorknob after shuffling your feet across a rug. It is also the property that produces lightning. Electric charge comes in two varieties: positive and negative.

The law of conservation of electric charge states that the total electric charge in a system is the same before and after any kind of change. Imagine a large cloud of gas with 1,000 positive (+) charges and 950 negative () charges. The total electrical charge on the gas would be 1,000+ + 950= 50+. Next, imagine that the gas is pushed together into a much smaller volume. Whatever else you may find out about this change, you can know one fact for certain: the total electric charge on the gas will continue to be 50+.

Conservation of momentum. Two of the most useful conservation laws apply to the property known as momentum. Linear momentum is defined as the product of an object's mass and its velocity. (Velocity is the rate at which the position of an object changes with time, including both the speed and the direction.) A 200-pound football player moving with a speed of 10 miles per hour has a linear momentum of 200 pounds × 10 miles per hour, or 2,000 pound-miles per hour. In comparison, a 100-pound sprinter running at a speed of 20 miles per hour has exactly the same liner momentum: 100 pounds × 20 miles per hour, or 2,000 pound-miles per hour.

Linear momentum is consumed in any change. For example, imagine a rocket ship about to be fired into space (Figure 1a). If the rocket ship is initially at rest, its speed is 0, so its momentum must be 0. No matter what its mass is, the linear momentum of the rocket is mass × 0 miles per hour = 0. The important fact that the conservation of linear momentum tells us is that, whatever else happens to the rocket ship, its final momentum will also be 0.

What happens when the rocket is fired, then, as in Figure 1b? Hot gases escape from the rear of the rocket ship. The momentum of those gases is equal to their total mass (call that mg) times their velocity (vg), or mgvg. We'll give this number a negative sign (mgvg) to indicate that the gases are escaping backward, or to the left.

The law of conservation of linear momentum says, then, that the rocket has to move in the opposite direction, to the right or the + direction, with a momentum of mgvg. That must be true because then mgvg(from the gases) plus +mgvg (from the rocket) = 0. If you know the mass of the rocket, you can find the speed with which it will travel to the right.

A second kind of momentum is angular momentum. The most familiar example of angular momentum is probably a figure skater spinning on the ice. The skater's angular momentum depends on three properties: her mass (or weight), the speed with which she is spinning, and the radius of her body.

At the beginning of a spin, the skater's arms may be extended outward, producing a large radius (the distance from the center of her body to the outermost part of his body). As she spins, she may pull her arms inward, bringing them to her side. What happens to the skater's angular momentum during the spin?

We can neglect the skater's mass, since she won't gain or lose any weight during the spin. The only factors to consider are the speed of her spin and her body radius. The law of conservation of angular momentum says that the product of these two quantities at the beginning of the spin (v1r1) must be the same as the product of the two quantities at the end of the spin (m2r2). So m1r1 = m2r2 must be true. But if the skater makes the radius of her body smaller, this equality can be true only if her velocity increases. This fact explains what you actually see on the ice. As a spinning skater pulls her arms in (and the body radius gets smaller), her spinning speed increases (and her velocity gets larger).

Conservation of parity. Conservation laws are now widely regarded as some of the most fundamental laws in all of nature. It was a great shock, therefore, when two American physicists, Val Lodgson Fitch (1923 ) and James Watson Cronin (1931 ), discovered in the mid-1960s that certain subatomic particles known as K-mesons appear to violate a conservation law. That law is known as the conservation of parity, which defines the basic symmetry of nature: that an object and its mirror image will behave the same way. Scientists have not yet fully explained this unexpected experimental result.

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## conservation laws

conservation laws, in physics, basic laws that together determine which processes can or cannot occur in nature; each law maintains that the total value of the quantity governed by that law, e.g., mass or energy, remains unchanged during physical processes. Conservation laws have the broadest possible application of all laws in physics and are thus considered by many scientists to be the most fundamental laws in nature.

Conservation of Classical Processes

Most conservation laws are exact, or absolute, i.e., they apply to all possible processes; a few conservation laws are only partial, holding for some types of processes but not for others. By the beginning of the 20th cent. physics had established conservation laws governing the following quantities: energy, mass (or matter), linear momentum, angular momentum, and electric charge. When the theory of relativity showed (1905) that mass was a form of energy, the two laws governing these quantities were combined into a single law conserving the total of mass and energy.

Conservation of Elementary Particle Properties

With the rapid development of the physics of elementary particles during the 1950s, new conservation laws were discovered that have meaning only on this subatomic level. Laws relating to the creation or annihilation of particles belonging to the baryon and lepton classes of particles have been put forward. According to these conservation laws, particles of a given group cannot be created or destroyed except in pairs, where one of the pair is an ordinary particle and the other is an antiparticle belonging to the same group. Recent work has raised the possibility that the proton, which is a type of baryon, may in fact be unstable and decay into lighter products; the postulated methods of decay would violate the conservation of baryon number. To date, however, no such decay has been observed, and it has been determined that the proton has a lifetime of at least 1031 years. Two partial conservation laws, governing the quantities known as strangeness and isotopic spin, have been discovered for elementary particles. Strangeness is conserved during the so-called strong interactions and the electromagnetic interactions, but not during the weak interactions associated with particle decay; isotopic spin is conserved only during the strong interactions.

Conservation of Natural Symmetries

One very important discovery has been the link between conservation laws and basic symmetries in nature. For example, empty space possesses the symmetries that it is the same at every location (homogeneity) and in every direction (isotropy); these symmetries in turn lead to the invariance principles that the laws of physics should be the same regardless of changes of position or of orientation in space. The first invariance principle implies the law of conservation of linear momentum, while the second implies conservation of angular momentum. The symmetry known as the homogeneity of time leads to the invariance principle that the laws of physics remain the same at all times, which in turn implies the law of conservation of energy. The symmetries and invariance principles underlying the other conservation laws are more complex, and some are not yet understood.

Three special conservation laws have been defined with respect to symmetries and invariance principles associated with inversion or reversal of space, time, and charge. Space inversion yields a mirror-image world where the "handedness" of particles and processes is reversed; the conserved quantity corresponding to this symmetry is called space parity, or simply parity, P. Similarly, the symmetries leading to invariance with respect to time reversal and charge conjugation (changing particles into their antiparticles) result in conservation of time parity, T, and charge parity, C. Although these three conservation laws do not hold individually for all possible processes, the combination of all three is thought to be an absolute conservation law, known as the CPT theorem, according to which if a given process occurs, then a corresponding process must also be possible in which particles are replaced by their antiparticles, the handedness of each particle is reversed, and the process proceeds in the opposite direction in time. Thus, conservation laws provide one of the keys to our understanding of the universe and its material basis.

Bibliography

See R. P. Feynman, The Character of Physical Law (1967); M. Gardner, The Ambidextrous Universe: Left, Right, and the Fall of Parity (rev. ed. 1969); S. Glashow, The Charm of Physics (1991).

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## conservation, laws of

conservation, laws of Physical laws stating that some property of a closed system is unaltered by change in the system; it is conserved. The most important are the laws of conservation of matter and energy. Mass and energy are interconvertible according to the equation E = mc2; what is conserved is the total mass and its equivalent in energy.