LAWS OF MOTION

CONCEPT

In all the universe, there are few ideas more fundamental than those expressed in the three laws of motion. Together these explain why it is relatively difficult to start moving, and then to stop moving; how much force is needed to start or stop in a given situation; and how one force relates to another. In their beauty and simplicity, these precepts are as compelling as a poem, and like the best of poetry, they identify something that resonates through all of life. The applications of these three laws are literally endless: from the planets moving through the cosmos to the first seconds of a car crash to the action that takes place when a person walks. Indeed, the laws of motion are such a part of daily life that terms such as inertia, force, and reaction extend into the realm of metaphor, describing emotional processes as much as physical ones.

HOW IT WORKS

The three laws of motion are fundamental to mechanics, or the study of bodies in motion. These laws may be stated in a number of ways, assuming they contain all the components identified by Sir Isaac Newton (1642-1727). It is on his formulation that the following are based:

The Three Laws of Motion

• First law of motion: An object at rest will remain at rest, and an object in motion will remain in motion, at a constant velocity unless or until outside forces act upon it.
• Second law of motion: The net force acting upon an object is a product of its mass multiplied by its acceleration.
• Third law of motion: When one object exerts a force on another, the second object exerts on the first a force equal in magnitude but opposite in direction.

Laws of Man vs. Laws of Nature

These, of course, are not "laws" in the sense that people normally understand that term. Human laws, such as injunctions against stealing or parking in a fire lane, are prescriptive: they state how the world should be. Behind the prescriptive statements of civic law, backing them up and giving them impact, is a mechanism—police, courts, and penalties—for ensuring that citizens obey.

A scientific law operates in exactly the opposite fashion. Here the mechanism for ensuring that nature "obeys" the law comes first, and the "law" itself is merely a descriptive statement concerning evident behavior. With human or civic law, it is clearly possible to disobey: hence, the justice system exists to discourage disobedience. In the case of scientific law, disobedience is clearly impossible—and if it were not, the law would have to be amended.

This is not to say, however, that scientific laws extend beyond their own narrowly defined limits. On Earth, the intrusion of outside forces—most notably friction—prevents objects from behaving perfectly according to the first law of motion. The common-sense definition of friction calls to mind, for instance, the action that a match makes as it is being struck; in its broader scientific meaning, however, friction can be defined as any force that resists relative motion between two bodies in contact.

The operations of physical forces on Earth are continually subject to friction, and this includes not only dry bodies, but liquids, for instance, which are subject to viscosity, or internal friction. Air itself is subject to viscosity, which prevents objects from behaving perfectly in accordance with the first law of motion. Other forces, most notably that of gravity, also come into play to stop objects from moving endlessly once they have been set in motion.

The vacuum of outer space presents scientists with the most perfect natural laboratory for testing the first law of motion: in theory, if they were to send a spacecraft beyond Earth's orbital radius, it would continue travelling indefinitely. But even this craft would likely run into another object, such as a planet, and would then be drawn into its orbit. In such a case, however, it can be said that outside forces have acted upon it, and thus the first law of motion stands.

The orbit of a satellite around Earth illustrates both the truth of the first law, as well as the forces that limit it. To break the force of gravity, a powered spacecraft has to propel the satellite into the exosphere. Yet once it has reached the frictionless vacuum, the satellite will move indefinitely around Earth without need for the motive power of an engine—it will get a "free ride," thanks to the first law of motion. Unlike the hypothetical spacecraft described above, however, it will not go spinning into space, because it is still too close to Earth. The planet's gravity keeps it at a fixed height, and at that height, it could theoretically circle Earth forever.

The first law of motion deserves such particular notice, not simply because it is the first law. Nonetheless, it is first for a reason, because it establishes a framework for describing the behavior of an object in motion. The second law identifies a means of determining the force necessary to move an object, or to stop it from moving, and the third law provides a picture of what happens when two objects exert force on one another.

The first law warrants special attention because of misunderstandings concerning it, which spawned a debate that lasted nearly twenty centuries. Aristotle (384-322 b.c.) was the first scientist to address seriously what is now known as the first law of motion, though in fact, that term would not be coined until about two thousand years after his death. As its title suggests, his Physics was a seminal work, a book in which Aristotle attempted to give form to, and thus define the territory of, studies regarding the operation of physical processes. Despite the great philosopher's many achievements, however, Physics is a highly flawed work, particularly with regard to what became known as his theory of impetus—that is, the phenomena addressed in the first law of motion.

Aristotle's Mistake

According to Aristotle, a moving object requires a continual application of force to keep it moving: once that force is no longer applied, it ceases to move. You might object that, when a ball is in flight, the force necessary to move it has already been applied: a person has thrown the ball, and it is now on a path that will eventually be stopped by the force of gravity. Aristotle, however, would have maintained that the air itself acts as a force to keep the ball in flight, and that when the ball drops—of course he had no concept of "gravity" as such—it is because the force of the air on the ball is no longer in effect.

These notions might seem patently absurd to the modern mind, but they went virtually unchallenged for a thousand years. Then in the sixth century a.d., the Byzantine philosopher Johannes Philoponus (c. 490-570) wrote a critique of Physics. In what sounds very much like a precursor to the first law of motion, Philoponus held that a body will keep moving in the absence of friction or opposition.

He further maintained that velocity is proportional to the positive difference between force and resistance—in other words, that the force propelling an object must be greater than the resistance. As long as force exceeds resistance, Philoponus held, a body will remain in motion. This in fact is true: if you want to push a refrigerator across a carpeted floor, you have to exert enough force not only to push the refrigerator, but also to overcome the friction from the floor itself.

The Arab philosophers Ibn Sina (Avicenna; 980-1037) and Ibn Bâjja (Avempace; fl. c. 1100) defended Philoponus's position, and the French scholar Peter John Olivi (1248-1298) became the first Western thinker to critique Aristotle's statements on impetus. Real progress on the subject, however, did not resume until the time of Jean Buridan (1300-1358), a French physicist who went much further than Philoponus had eight centuries earlier.

In his writing, Buridan offered an amazingly accurate analysis of impetus that prefigured all three laws of motion. It was Buridan's position that one object imparts to another a certain amount of power, in proportion to its velocity and mass, that causes the second object to move a certain distance. This, as will be shown below, was amazingly close to actual fact. He was also correct in stating that the weight of an object may increase or decrease its speed, depending on other circumstances, and that air resistance slows an object in motion.

The true breakthrough in understanding the laws of motion, however, came as the result of work done by three extraordinary men whose lives stretched across nearly 250 years. First came Nicolaus Copernicus (1473-1543), who advanced what was then a heretical notion: that Earth, rather than being the center of the universe, revolved around the Sun along with the other planets. Copernicus made his case purely in terms of astronomy, however, with no direct reference to physics.

Galileo's Challenge: The Copernican Model

Galileo Galilei (1564-1642) likewise embraced a heliocentric (Sun-centered) model of the universe—a position the Church forced him to renounce publicly on pain of death. As a result of his censure, Galileo realized that in order to prove the Copernican model, it would be necessary to show why the planets remain in motion as they do. In explaining this, he coined the term inertia to describe the tendency of an object in motion to remain in motion, and an object at rest to remain at rest. Galileo's observations, in fact, formed the foundation for the laws of motion.

In the years that followed Galileo's death, some of the world's greatest scientific minds became involved in the effort to understand the forces that kept the planets in motion around the Sun. Among them were Johannes Kepler (1571-1630), Robert Hooke (1635-1703), and Edmund Halley (1656-1742). As a result of a dispute between Hooke and Sir Christopher Wren (1632-1723) over the subject, Halley brought the question to his esteemed friend Isaac Newton. As it turned out, Newton had long been considering the possibility that certain laws of motion existed, and these he presented in definitive form in his Principia (1687).

The impact of the Newton's book, which included his observations on gravity, was nothing short of breathtaking. For the next three centuries, human imagination would be ruled by the Newtonian framework, and only in the twentieth century would the onset of new ideas reveal its limitations. Yet even today, outside the realm of quantum mechanics and relativity theory—in other words, in the world of everyday experience—Newton's laws of motion remain firmly in place.

REAL-LIFE APPLICATIONS

The First Law of Motion in a Car Crash

It is now appropriate to return to the first law of motion, as formulated by Newton: an object at rest will remain at rest, and an object in motion will remain in motion, at a constant velocity unless or until outside forces act upon it. Examples of this first law in action are literally unlimited.

One of the best illustrations, in fact, involves something completely outside the experience of Newton himself: an automobile. As a car moves down the highway, it has a tendency to remain in motion unless some outside force changes its velocity. The latter term, though it is commonly understood to be the same as speed, is in fact more specific: velocity can be defined as the speed of an object in a particular direction.

In a car moving forward at a fixed rate of 60 MPH (96 km/h), everything in the car—driver, passengers, objects on the seats or in the trunk—is also moving forward at the same rate. If that car then runs into a brick wall, its motion will be stopped, and quite abruptly. But though its motion has stopped, in the split seconds after the crash it is still responding to inertia: rather than bouncing off the brick wall, it will continue plowing into it.

What, then, of the people and objects in the car? They too will continue to move forward in response to inertia. Though the car has been stopped by an outside force, those inside experience that force indirectly, and in the fragment of time after the car itself has stopped, they continue to move forward—unfortunately, straight into the dashboard or windshield.

It should also be clear from this example exactly why seatbelts, headrests, and airbags in automobiles are vitally important. Attorneys may file lawsuits regarding a client's injuries from airbags, and homespun opponents of the seatbelt may furnish a wealth of anecdotal evidence concerning people who allegedly died in an accident because they were wearing seatbelts; nonetheless, the first law of motion is on the side of these protective devices.

The admittedly gruesome illustration of a car hitting a brick wall assumes that the driver has not applied the brakes—an example of an outside force changing velocity—or has done so too late. In any case, the brakes themselves, if applied too abruptly, can present a hazard, and again, the significant factor here is inertia. Like the brick wall, brakes stop the car, but there is nothing to stop the driver and/or passengers. Nothing, that is, except protective devices: the seat belt to keep the person's body in place, the airbag to cushion its blow, and the headrest to prevent whiplash in rear-end collisions.

Inertia also explains what happens to a car when the driver makes a sharp, sudden turn. Suppose you are is riding in the passenger seat of a car moving straight ahead, when suddenly the driver makes a quick left turn. Though the car's tires turn instantly, everything in the vehicle—its frame, its tires, and its contents—is still responding to inertia, and therefore "wants" to move forward even as it is turning to the left.

As the car turns, the tires may respond to this shift in direction by squealing: their rubber surfaces were moving forward, and with the sudden turn, the rubber skids across the pavement like a hard eraser on fine paper. The higher the original speed, of course, the greater the likelihood the tires will squeal. At very high speeds, it is possible the car may seem to make the turn "on two wheels"—that is, its two outer tires. It is even possible that the original speed was so high, and the turn so sharp, that the driver loses control of the car.

Here inertia is to blame: the car simply cannot make the change in velocity (which, again, refers both to speed and direction) in time. Even in less severe situations, you are likely to feel that you have been thrown outward against the rider's side door. But as in the car-and-brick-wall illustration used earlier, it is the car itself that first experiences the change in velocity, and thus it responds first. You, the passenger, then, are moving forward even as the car has turned; therefore, rather than being thrown outward, you are simply meeting the leftward-moving door even as you push forward.

From Parlor Tricks to Space Ships

It would be wrong to conclude from the carrelated illustrations above that inertia is always harmful. In fact it can help every bit as much as it can potentially harm, a fact shown by two quite different scenarios.

The beneficial quality to the first scenario may be dubious: it is, after all, a mere parlor trick, albeit an entertaining one. In this famous stunt, with which most people are familiar even if they have never seen it, a full table setting is placed on a table with a tablecloth, and a skillful practitioner manages to whisk the cloth out from under the dishes without upsetting so much as a glass. To some this trick seems like true magic, or at least sleight of hand; but under the right conditions, it can be done. (This information, however, carries with it the warning, "Do not try this at home!")

To make the trick work, several things must align. Most importantly, the person doing it has to be skilled and practiced at performing the feat. On a physical level, it is best to minimize the friction between the cloth and settings on the one hand, and the cloth and table on the other. It is also important to maximize the mass (a property that will be discussed below) of the table settings, thus making them resistant to movement. Hence, inertia—which is measured by mass—plays a key role in making the tablecloth trick work.

You might question the value of the tablecloth stunt, but it is not hard to recognize the importance of the inertial navigation system (INS) that guides planes across the sky. Prior to the 1970s, when INS made its appearance, navigation techniques for boats and planes relied on reference to external points: the Sun, the stars, the magnetic North Pole, or even nearby areas of land. This created all sorts of possibilities for error: for instance, navigation by magnet (that is, a compass) became virtually useless in the polar regions of the Arctic and Antarctic.

By contrast, the INS uses no outside points of reference: it navigates purely by sensing the inertial force that results from changes in velocity. Not only does it function as well near the poles as it does at the equator, it is difficult to tamper with an INS, which uses accelerometers in a sealed, shielded container. By contrast, radio signals or radar can be "confused" by signals from the ground—as, for instance, from an enemy unit during wartime.

As the plane moves along, its INS measures movement along all three geometrical axes, and provides a continuous stream of data regarding acceleration, velocity, and displacement. Thanks to this system, it is possible for a pilot leaving California for Japan to enter the coordinates of a half-dozen points along the plane's flight path, and let the INS guide the autopilot the rest of the way.

Yet INS has its limitations, as illustrated by the tragedy that occurred aboard Korean Air Lines (KAL) Flight 007 on September 1, 1983. The plane, which contained 269 people and crew members, departed Anchorage, Alaska, on course for Seoul, South Korea. The route they would fly was an established one called "R-20," and it appears that all the information regarding their flight plan had been entered correctly in the plane's INS.

This information included coordinates for internationally recognized points of reference, actually just spots on the northern Pacific with names such as NABIE, NUKKS, NEEVA, and so on, to NOKKA, thirty minutes east of Japan. Yet, just after passing the fishing village of Bethel, Alaska, on the Bering Sea, the plane started to veer off course, and ultimately wandered into Soviet airspace over the Kamchatka Peninsula and later Sakhalin Island. There a Soviet Su-15 shot it down, killing all the plane's passengers.

In the aftermath of the Flight 007 shoot-down, the Soviets accused the United States and South Korea of sending a spy plane into their airspace. (Among the passengers was Larry McDonald, a staunchly anti-Communist Congressman from Georgia.) It is more likely, however, that the tragedy of 007 resulted from errors in navigation which probably had something to do with the INS. The fact is that the R-20 flight plan had been designed to keep aircraft well out of Soviet airspace, and at the time KAL 007 passed over Kamchatka, it should have been 200 mi (320 km) to the east—over the Sea of Japan.

Among the problems in navigating a transpacific flight is the curvature of the Earth, combined with the fact that the planet continues to rotate as the aircraft moves. On such long flights, it is impossible to "pretend," as on a short flight, that Earth is flat: coordinates have to be adjusted for the rounded surface of the planet. In addition, the flight plan must take into account that (in the case of a flight from California to Japan), Earth is moving eastward even as the plane moves westward. The INS aboard KAL 007 may simply have failed to correct for these factors, and thus the error compounded as the plane moved further. In any case, INS will eventually be rendered obsolete by another form of navigation technology: the global positioning satellite (GPS) system.

Understanding Inertia

From examples used above, it should be clear that inertia is a more complex topic than you might immediately guess. In fact, inertia as a process is rather straightforward, but confusion regarding its meaning has turned it into a complicated subject.

In everyday terminology, people typically use the word inertia to describe the tendency of a stationary object to remain in place. This is particularly so when the word is used metaphorically: as suggested earlier, the concept of inertia, like numerous other aspects of the laws of motion, is often applied to personal or emotional processes as much as the physical. Hence, you could say, for instance, "He might have changed professions and made more money, but inertia kept him at his old job." Yet you could just as easily say, for example, "He might have taken a vacation, but inertia kept him busy." Because of the misguided way that most people use the term, it is easy to forget that "inertia" equally describes a tendency toward movement or nonmovement: in terms of Newtonian mechanics, it simply does not matter.

The significance of the clause "unless or until outside forces act upon it" in the first law indicates that the object itself must be in equilibrium—that is, the forces acting upon it must be balanced. In order for an object to be in equilibrium, its rate of movement in a given direction must be constant. Since a rate of movement equal to 0 is certainly constant, an object at rest is in equilibrium, and therefore qualifies; but also, any object moving in a constant direction at a constant speed is also in equilibrium.

The Second Law: Force, Mass, Acceleration

As noted earlier, the first law of motion deserves special attention because it is the key to unlocking the other two. Having established in the first law the conditions under which an object in motion will change velocity, the second law provides a measure of the force necessary to cause that change.

Understanding the second law requires defining terms that, on the surface at least, seem like a matter of mere common sense. Even inertia requires additional explanation in light of terms related to the second law, because it would be easy to confuse it with momentum.

The measure of inertia is mass, which reflects the resistance of an object to a change in its motion. Weight, on the other hand, measures the gravitational force on an object. (The concept of force itself will require further definition shortly.) Hence a person's mass is the same everywhere in the universe, but their weight would differ from planet to planet.

This can get somewhat confusing when you attempt to convert between English and metric units, because the pound is a unit of weight or force, whereas the kilogram is a unit of mass. In fact it would be more appropriate to set up kilograms against the English unit called the slug (equal to 14.59 kg), or to compare pounds to the metric unit of force, the newton (N), which is equal to the acceleration of one meter per second per second on an object of 1 kg in mass.

Hence, though many tables of weights and measures show that 1 kg is equal to 2.21 lb, this is only true at sea level on Earth. A person with a mass of 100 kg on Earth would have the same mass on the Moon; but whereas he might weigh 221 lb on Earth, he would be considerably lighter on the Moon. In other words, it would be much easier to lift a 221-lb man on the Moon than on Earth, but it would be no easier to push him aside.

To return to the subject of momentum, whereas inertia is measured by mass, momentum is equal to mass multiplied by velocity. Hence momentum, which Newton called "quantity of motion," is in effect inertia multiplied by velocity. Momentum is a subject unto itself; what matters here is the role that mass (and thus inertia) plays in the second law of motion.

According to the second law, the net force acting upon an object is a product of its mass multiplied by its acceleration. The latter is defined as a change in velocity over a given time interval: hence acceleration is usually presented in terms of "feet (or meters) per second per second"—that is, feet or meters per second squared. The acceleration due to gravity is 32 ft (9.8 m) per second per second, meaning that as every second passes, the speed of a falling object is increasing by 32 ft (9.8 m) per second.

The second law, as stated earlier, serves to develop the first law by defining the force necessary to change the velocity of an object. The law was integral to the confirming of the Copernican model, in which planets revolve around the Sun. Because velocity indicates movement in a single (straight) direction, when an object moves in a curve—as the planets do around the Sun—it is by definition changing velocity, or accelerating. The fact that the planets, which clearly possessed mass, underwent acceleration meant that some force must be acting on them: a gravitational pull exerted by the Sun, most massive object in the solar system.

Gravity is in fact one of four types of force at work in the universe. The others are electromagnetic interactions, and "strong" and "weak" nuclear interactions. The other three were unknown to Newton—yet his definition of force is still applicable. Newton's calculation of gravitational force (which, like momentum, is a subject unto itself) made it possible for Halley to determine that the comet he had observed in 1682—the comet that today bears his name—would reappear in 1758, as indeed it has for every 75-76 years since then. Today scientists use the understanding of gravitational force imparted by Newton to determine the exact altitude necessary for a satellite to remain stationary above the same point on Earth's surface.

The second law is so fundamental to the operation of the universe that you seldom notice its application, and it is easiest to illustrate by examples such as those above—of astronomers and physicists applying it to matters far beyond the scope of daily life. Yet the second law also makes it possible, for instance, to calculate the amount of force needed to move an object, and thus people put it into use every day without knowing that they are doing so.

The Third Law: Action and Reaction

As with the second law, the third law of motion builds on the first two. Having defined the force necessary to overcome inertia, the third law predicts what will happen when one force comes into contact with another force. As the third law states, when one object exerts a force on another, the second object exerts on the first a force equal in magnitude but opposite in direction.

Unlike the second law, this one is much easier to illustrate in daily life. If a book is sitting on a table, that means that the book is exerting a force on the table equal to its mass multiplied by its rate of acceleration. Though it is not moving, the book is subject to the rate of gravitational acceleration, and in fact force and weight (which is defined as mass multiplied by the rate of acceleration due to gravity) are the same. At the same time, the table pushes up on the book with an exactly equal amount of force—just enough to keep it stationary. If the table exerted more force that the book—in other words, if instead of being an ordinary table it were some sort of pneumatic press pushing upward—then the book would fly off the table.

There is no such thing as an unpaired force in the universe. The table rests on the floor just as the book rests on it, and the floor pushes up on the table with a force equal in magnitude to that with which the table presses down on the floor. The same is true for the floor and the supporting beams that hold it up, and for the supporting beams and the foundation of the building, and the building and the ground, and so on.

These pairs of forces exist everywhere. When you walk, you move forward by pushing backward on the ground with a force equal to your mass multiplied by your rate of downward gravitational acceleration. (This force, in other words, is the same as weight.) At the same time, the ground actually pushes back with an equal force. You do not perceive the fact that Earth is pushing you upward, simply because its enormous mass makes this motion negligible—but it does push.

If you were stepping off of a small unmoored boat and onto a dock, however, something quite different would happen. The force of your leap to the dock would exert an equal force against the boat, pushing it further out into the water, and as a result, you would likely end up in the water as well. Again, the reaction is equal and opposite; the problem is that the boat in this illustration is not fixed in place like the ground beneath your feet.

Differences in mass can result in apparently different reactions, though in fact the force is the same. This can be illustrated by imagining a mother and her six-year-old daughter skating on ice, a relatively frictionless surface. Facing one another, they push against each other, and as a result each moves backward. The child, of course, will move backward faster because her mass is less than that of her mother. Because the force they exerted is equal, the daughter's acceleration is greater, and she moves farther.

Ice is not a perfectly frictionless surface, of course: otherwise, skating would be impossible. Likewise friction is absolutely necessary for walking, as you can illustrate by trying to walk on a perfectly slick surface—for instance, a skating rink covered with oil. In this situation, there is still an equally paired set of forces—your body presses down on the surface of the ice with as much force as the ice presses upward—but the lack of friction impedes the physical process of pushing off against the floor.

It will only be possible to overcome inertia by recourse to outside intervention, as for instance if someone who is not on the ice tossed out a rope attached to a pole in the ground. Alternatively, if the person on the ice were carrying a heavy load of rocks, it would be possible to move by throwing the rocks backward. In this situation, you are exerting force on the rock, and this backward force results in a force propelling the thrower forward.

This final point about friction and movement is an appropriate place to close the discussion on the laws of motion. Where walking or skating are concerned—and in the absence of a bag of rocks or some other outside force—friction is necessary to the action of creating a backward force and therefore moving forward. On the other hand, the absence of friction would make it possible for an object in movement to continue moving indefinitely, in line with the first law of motion. In either case, friction opposes inertia.

The fact is that friction itself is a force. Thus, if you try to slide a block of wood across a floor, friction will stop it. It is important to remember this, lest you fall into the fallacy that bedeviled Aristotle's thinking and thus confused the world for many centuries. The block did not stop moving because the force that pushed it was no longer being applied; it stopped because an opposing force, friction, was greater than the force that was pushing it.

WHERE TO LEARN MORE

Ardley, Neil. The Science Book of Motion. San Diego: Harcourt Brace Jovanovich, 1992.

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.

Chase, Sara B. Moving to Win: The Physics of Sports. New York: Messner, 1977.

Fleisher, Paul. Secrets of the Universe: Discovering the Universal Laws of Science. Illustrated by Patricia A. Keeler. New York: Atheneum, 1987.

"The Laws of Motion." How It Flies (Web site). <http://www.monmouth.com/~jsd/how/htm/motion.html> (February 27, 2001).

Newton, Isaac (translated by Andrew Motte, 1729). The Principia (Web site). <http://members.tripod.com/~gravitee/principia.html> (February 27, 2001).

Newton's Laws of Motion (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/newtlaws/newtloc.html> (February 27, 2001).

"Newton's Laws of Motion." Dryden Flight Research Cen ter, National Aeronautics and Space Administration (NASA) (Web site). <http://www.dfrc.nasa.gov/trc/saic/newton.html> (February 27, 2001).

"Newton's Laws of Motion: Movin' On." Beyond Books (Web site). <http://www.beyondbooks.com/psc91/4.asp> (February 27, 2001).

Roberts, Jeremy. How Do We Know the Laws of Motion? New York: Rosen, 2001.

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

KEY TERMS

ACCELERATION:

A change in velocity over a given time period.

EQUILIBRIUM:

A situation in which the forces acting upon an object are in balance.

FRICTION:

Any force that resists the motion of body in relation to another with which it is in contact.

INERTIA:

The tendency of an object in motion to remain in motion, and of an object at rest to remain at rest.

MASS:

A measure of inertia, indicating the resistance of an object to a change in its motion—including a change in velocity. A kilogram is a unit of mass, whereas a pound is a unit of weight. The mass of an object remains the same throughout the universe, whereas its weight is a function of gravity on any given planet.

MECHANICS:

The study of bodies in motion.

MOMENTUM:

The product of mass multiplied by velocity.

SPEED:

The rate at which the position of an object changes over a given period of time.

VELOCITY:

The speed of an object in a particular direction.

VISCOSITY:

The internal friction in a fluid that makes it resistant to flow.

WEIGHT:

A measure of the gravitational force on an object. A pound is a unit of weight, whereas a kilogram is a unit ofmass. Weight thus would change from planet to planet, whereas mass remains constant throughout the universe.

Newton's laws of motion

Earthly and heavenly motions were of great interest to Newton. Applying an acute sense for asking the right questions with reasoning, Newton formulated three laws which allowed a complete analysis (mathematical) of dynamics, relating all aspects of motion to basic causes, force and mass . So influential was Newton's work that it is referred to as the first revolution in physics .

First law of motion

Galileo's observation that without friction a body would tend to move forever challenged Aristotle's notion that the natural state of motion on Earth was one of rest. Galileo deduced that it was a property of matter to maintain its state of motion, a property he called inertia. Newton, grasping the meaning of inertia and recognizing that Aristotle's reference to what keeps a body in motion (outside influence) really should have been what changes a body's state of motion, set forth a first law of motion which states: A body at rest remains at rest or a body in constant motion remains in constant motion along a straight line unless acted on by an external influence, called force.

Examples of the first law

(1) Why use seat belts? Riding in a car you and the car have the same motion. When the brakes are applied, the brakes stop the car. What stops you? Eventually the steering wheel, the dashboard, or the window unless they are replaced by a seat belt, which stops your body. When the accelerator is depressed with the car in gear the motor turns the wheels and the car moves forward. What moves you forward? As the car moves forward the seatback comes forward, contacts, you and pushes you forward.

(2) While you are riding in the front passenger seat of a car, the driver suddenly turns left. What about you? You continue to move in a straight line until the door to your right, turning left, eventually runs into you. In the car it may appear to you that you slid outward and hit the door.

Second law of motion

The first law of motion concentrates on a state of constant motion but adds unless an outside influence, force, acts on it. Force produces a change in the state of motion (velocity describes a body's motion); that is, an acceleration . Newton found that the greater a body's mass the greater the force required to overcome its inertia and mass is taken as a quantitative measure of a body's inertia. He also found that applying equal force to two different masses, the ratio of their accelerations was inversely proportional to the ratio of their masses. Newton's second law of motion is thus stated: A net force acting on a body produces an acceleration; the acceleration is inversely proportional to its mass and directly proportional to the net force and in the same direction.

This law can be put mathematically F = ma where F is the net force, m is the mass, and a the acceleration. The second law is a cause-effect relationship. The net force acting on a body is determined from all forces acting and the resultant acceleration calculated (assuming a known mass). From the acceleration, velocity and distance traveled can be determined for any time .

Applications of the second law

(1) Objects, when released, fall to the ground due to the earth's attraction. Newton's universal law of gravity gave the force of attraction between two masses, m and M, as F =GmM/R2 where G is the gravitational constant and R is the distance between mass centers. This force, weight, produces gravitational acceleration g, thus weight = GmM/R2 = mg(2nd Law) giving g = GM/R2. This relationship holds universally. For all objects at the earth's surface, g =32 ft/sec/sec or 9.8 m/sec/sec downward and on Jupiter 84 ft/sec/sec. Since the dropped object's mass does not appear, g is the same for all objects. Falling objects have their velocity changed downward at the rate of 32 ft/sec each second on earth. Falling from rest, at the end of one second the velocity is 32 ft/sec, after 2 seconds 64 ft/sec, after 3 seconds 96 ft/sec, etc.

For objects thrown upward, gravitational acceleration is still 32 ft/sec/sec downward. A ball thrown upward with an initial velocity of 80 ft/sec has a velocity after one second of 80-32= 48 ft/sec, after two seconds 48-32= 16 ft/sec, and after three seconds 16-32= -16 ft/sec (now downward), etc. At 2.5 seconds the ball had a zero velocity and after another 2.5 seconds it hits the ground with a velocity of 80 ft/sec downward. The up and down motion is symmetrical.

(2) Friction, a force acting between two bodies in contact, is parallel to the surface and opposite the motion (or tendency to move). By the second law, giving a mass of one kilogram (kg) an acceleration of 1 m/sec/sec requires a force of one Newton (N). However, if friction were 3 N, a force of 4 N must be applied to give the same acceleration. The net force is 4N (applied by someone) minus 3N (friction) or 1N.

Free fall, example (1), assumed no friction. If there were atmospheric friction it would be directed upward since friction always opposes the motion. Air friction is proportional to the velocity; as the velocity increases the friction force (upward) becomes larger. The net force (weight minus friction) and the acceleration are less than due to gravity alone. Therefore, the velocity increases less rapidly, becoming constant when the friction force equals the weight of the falling object (net force=0). This velocity is called the terminal velocity. A greater weight requires a longer time for air friction to equal the weight, resulting in a larger terminal velocity.

(3) A contemporary and friend of Newton, Halley, observed a comet in 1682 and suspected others had observed it many times before. Using Newton's new mechanics (laws of motion and universal law of gravity) Halley calculated that the comet would reappear at Christmas, 1758. Although Halley was dead, the comet reappeared at that time and became known as Halley's comet . This was a great triumph for Newtonian mechanics.

Using Newton's universal law of gravity (see example 1) in the second law results in a general solution (requiring calculus ) in which details of the paths of motion (velocity, acceleration, period) are given in terms of G, M, and distance of separation.

While these results agreed with planetary motion known at the time there was now an explanation for differences in motions. These solutions were equally valid for applying to any systems body: Earth's moon , Jupiter's moons, galaxies, truly universal.

(4) Much of Newton's work involved rotational motion, particularly circular motion. The velocity's direction constantly changes, requiring a centripetal acceleration. This centripetal acceleration requires a net force, the centripetal force, acting toward the center of motion. Centripetal acceleration is given by a(central)=v2/R where v is the velocity's magnitude and R is the radius of the motion. Hence, the centripetal force F(central) = mv2/R, where m is the mass. These relationships hold for any case of circular motion and furnish the basis for "thrills" experienced on many amusement park rides such as ferris wheels, loop-the-loops, merry-go-rounds, and any other means for changing your direction rather suddenly. Some particular examples follow.

(a.) Newton asked himself why the moon did not fall to Earth like other objects. Falling with the same acceleration of gravity as bodies at Earth's surface, it would have hit Earth. With essentially uniform circular motion about Earth, the moon's centripetal acceleration and force must be due to Earth's gravity. With gravitational force providing centripetal force, the centripetal acceleration is a(central) = GM/R2 (acceleration of gravity in example 1 above). Since the moon is about 60 times further from Earth's center than the earth's surface, the acceleration of gravity of the moon is about. 009 ft/sec/sec. In one second the moon would fall about.06 inch but while doing this it is also moving away from the earth with the result that at the end of one second the moon is at the same distance from the earth, R.

(b.) With the gravitational force responsible for centripetal acceleration, equating the two acceleration expressions given above gives the magnitude of the velocity as v2 = GM/R with the same symbol meanings. For the moon in (a) its velocity would be about 2,250 MPH. This relationship can be universally applied.

Long ago it was recognized that this analysis could be applied to artificial "moons" or satellites. If a satellite could be made to encircle the earth at about 200 mi it must be given a tangential velocity of about 18,000 MPH and it would encircle the earth every 90 seconds; astronauts have done this many times since 1956, 300 years after Newton gave the means for predicting the necessary velocities.

It was asked: what velocity and height must a satellite have so that it remains stationary above the same point on Earth's surface; that is, have the same rotation period, one day, as the earth. Three such satellites, placed 120 degrees apart around the earth, could make instantaneous communication with all points on the earth's surface possible. From the fact that period squared is proportional to the cube of the radius and the above periods of the moon and satellite and the moon's distance, it is found that the communication satellite would have to be located 26,000 mi from earth's center or 22,000 mi above the surface. Its velocity must be about 6,800 MPH. Many such satellites are now in space around the earth.

(c.) When a car rounds a curve what keeps it on the road? Going around a curve requires a centripetal force to furnish the centripetal acceleration, changing its direction. If there is not, the car continues in a straight line (first law) moving outward relative to the road. Friction, opposing outward motion, would be inward and the inward acceleration a(cent) =friction/mass = v2/R. Each radius has a predictable velocity for which the car can make the curve. A caution must be added: when it is raining, friction is reduced and a lower velocity is needed to make the curve safely.

Third law of motion or law of action-reaction

Newton questioned the interacting force an outside agent exerted on another to change its state of motion. He concluded that this interaction was mutual so that when you exert a force on something you get the feeling the other is exerting a force on you. Newton's third law of motion states: When one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body.

In the second law, only forces exerted on a body are important in determining its acceleration. The third law speaks about a pair of forces equal in magnitude and opposite in direction which are exerted on and by two different bodies. This law is useful in determining forces acting on an object by knowing forces it exerts. For example, a book sitting on a table has a net force of zero. Therefore, an upward force equal to its weight must be exerted by the table on the book. According to the third law the book exerts an equal force downward on the table. When two objects are in contact they exert equal and opposite forces on each other and these forces are perpendicular to the contacting surface.

Examples of the third law

(1) What enables us to walk? To move forward parallel to the floor we must push backward on the floor with one foot. By the third law, the floor pushes forward, moving us forward. Then the process is repeated with the other foot, etc. This cannot occur unless there is friction between the foot and floor and on a frictionless surface we would not be able to walk.

(2) How can airplanes fly at high altitudes and space crafts be propelled? High altitude airplanes utilize jet engines; that is, engines burn fuel at high temperatures and expel it backward. In expelling the burnt fuel a force is exerted backward on it and it exerts an equal forward force on the plane . The same analysis applies to space crafts.

(3) A father takes his eight-year-old daughter to skate. The father and the girl stand at rest facing each other. The daughter pushes the father backwards. What happens? Whatever force the daughter exerts on her father he exerts in the opposite direction equally on her. Since the father has a larger mass his acceleration will be less than the daughter's. With the larger acceleration the daughter will move faster and travel farther in a given time.

Resources

books

Cohen, I. Bernard. Introduction to Newton's Principia. Lincoln, NE: iUniverse, 1999.

Hagen, Robert M. and Trefil, James. Science Matters. New York: Doubleday, 1991.

Hewitt, Paul. Conceptual Physics. Englewood Cliffs, NJ: Prentice Hall, 2001.

Hobson, Art. Physics Concepts and Connections. Englewood Cliffs, NJ: Prentice Hall, 1995.

Kirkpatrick, Larry and Gerald Wheeler. Physics: A World View. 2nd ed. Chicago: Saunders, 1995.

Munson, Bruce, et al. Fundamentals of Mechanics. 4th ed. New York: John Wiley and Sons, 2002.

Teller, Edward, Teller, Wendy, and Talley, Wilson. Conversations On The Dark Secrets Of Physics. New York: Plenum Press, 1991.

Billy W. Sloope

KEY TERMS

Centripetal acceleration

—Produces a change in the direction of velocity and always perpendicular to the velocity vector. This, in turn is caused by a centripetal force.

Force

—Influence exerted on an object by an outside agent which produces an acceleration changing the object's state of motion.

Inertia

—Property of matter whereby any change in state of motion is opposed. Quantitatively measured by mass.

Laws of Motion

History

Newton’s Three Laws

Resources

What makes a bird fly? A person run? A judo expert flip a heavier opponent? The Earth orbit the sun? Three deceptively simple laws first stated by English physicist and mathematician Sir Isaac Newton (1642–1727) in the seventeenth century govern these and any other motions. These three laws of motion when coupled with Newton’s law of gravity form the basis for explaining both the motions seen on the Earth and the motions of the heavenly bodies.

History

In the sixteenth century, Polish astronomer Nicolaus Copernicus (1473–1543) suggested that Earth and other planets orbited the sun, but his model contained no physics. It did not say why the planets should orbit the sun. Galileo was censured by the Catholic Church and forced to recant his belief in the Copernican model. He then realized that to ultimately win, the Copernican model needed a physical basis. Galileo therefore started to quietly develop the new physics needed to explain planetary motions. Newton, who was born the year Galileo died, built on the foundation laid by Galileo. The resulting edifice, Newton’s laws, was a grand synthesis that for the first time explained motions both on Earth and in the heavens with a unified set of laws.

Newton’s Three Laws

Slide a block of wood across a level uncarpeted floor and notice its behavior. The block continues to move as long as one applies a force. When the force stops, the block stops moving. The block will continue to slide for a while after one stops applying a force. The pushing is not the only force acting on the block. There is also a frictional force opposing the motion. The block sliding across the floor stops because this frictional force acts on it. The block on an icy surface takes longer to stop because there is less frictional force. If one could slide the block across a surface with absolutely no friction, it would never stop. The block would keep moving until some outside force, such as the wall of the room, stopped it. A block on a level surface, without application of forces will not move unless something applies an outside force; it will remain there at rest forever.

The first of Newton’s laws states an object will continue its motion at a constant velocity until an outside force acts on it. The block has a tendency to continue in its state of motion, whatever that state might be, until some force changes that state of motion. This tendency to continue in a state of motion is called the object’s inertia. An object at rest simply has a constant velocity of zero, so it needs an outside force to start moving. The physicist’s definition of velocity includes both speed and direction, so any deviation from straight-line motion is a change in velocity and will require an outside force. The inertia of any object will cause it to continue to move at a constant (in a straight line) velocity (or stay at rest) until an outside force acts on it.

A block will slide more easily than, for instance, a refrigerator because it has less mass. Newton’s first law says that a force is needed to change the velocity of an object; the second law tells how much force. Any change in velocity (speed up, slow down, or change direction) is an acceleration. For the common case where the mass does not change, Newton’s second law states that the force required is equal to the accelerated mass times the acceleration (Force = Mass × Acceleration). It is harder to slide the refrigerator than the block across the floor because the greater mass requires a greater force to accelerate it from rest.

KEY TERMS

Acceleration —The rate at which the velocity of an object changes over time.

Force —Influence exerted on an object by an outside agent that produces an acceleration changing the object’s state of motion.

Inertia —The tendency of an object in motion to remain in motion, and the tendency of an object at rest to remain at rest.

Mass —A measure of the amount of matter in kilograms. Related both to the resistance to the change in motion and to the amount of gravitational force.

Velocity —The speed and direction of a moving object.

A force in the same direction as the velocity increases the velocity; in the opposite direction, decreases it. A force perpendicular to the velocity changes the direction of motion. Occasionally the accelerated mass changes. In this case, the force is equal to the rate at which the momentum changes with time.

Newton’s third law states that for every action there is an equal and opposite reaction. The action and reaction are equal and opposite forces forming an action reaction pair. If one sits in a chair, the Earth’s gravity pulls down. The reaction is that the human body pulls the Earth up with exactly the same amount of force. The action reaction pair is: human on Earth, Earth on human. The reaction is NOT, as is often thought, the floor or chair holding the body up. Not all equal and opposite forces form an action reaction pair.

Newton’s three laws of motion revolutionized physics. For the first time the same simple set of laws explained a wide variety of apparently unrelated types of motion both on Earth and in the heavens. Not until the twentieth century were these laws surpassed by quantum mechanics and relativity for the special cases of subatomic particles, motion near the speed of light and strong gravitational fields.

See also Gravity and gravitation; Relativity, general.

Resources

BOOKS

Feynman, Richard Phillips. The Feynman Lectures on Physics.

San Francisco, CA: Pearson/Addison-Wesley, 2006. Folan, Lorcan M. Modern Physics and Technology for

Undergraduates. River Edge, NJ: World Scientific, 2003.

Griffith, W. Thomas. The Physics of Everyday Phenomena:

A Conceptual Introduction to Physics. Boston, MA: McGraw-Hill, 2004.

Hewitt, Paul. Conceptual Physics. New York: Prentice Hall,

2001.

Serway, Raymond, Jerry S. Faughn, and Clement J. Moses.

College Physics. 6th ed. Pacific Grove, CA: Brooks/Cole, 2002.

Young, Hugh D. Sears and Zemansky’s University Physics.

San Francisco, CA: Pearson Addison Wesley, 2004.

Paul A. Heckert

Laws of motion

The term laws of motion generally refers to three statements originally devised by English physicist Isaac Newton (1642–1727) in the 1680s. These laws, along with Newton's law of gravitation, are generally considered to be the ultimate solution to a problem that had troubled scholars for more than 2,000 years: motion.

History

Examples of motion are everywhere in the world around us. What makes a rock fall off a cliff? How does a skate slide across an icy surface? What keeps the planets in their orbits around the Sun? It is only natural, then, that questions about motion were foremost in the minds of ancient philosophers and physicists.

Greek philosopher Aristotle (384–322 b.c.), for example, tried to find the causes of motion. He said that some forms of motion were "natural." Rocks fall toward the ground because the ground is a natural place for rocks to be. Objects rise into the air when they are heated because the Sun is hot, and so it is natural for heat to rise.

Aristotle classified other forms of motion as "violent" because they were not natural to his way of thinking. For example, shooting an arrow through space produced violent motion since the arrow's natural tendency was to fall straight down toward Earth.

Aristotle's thinking about motion dominated Western thought for 2,000 years. Unfortunately, his ideas were not really very productive, and scholars tried continually to improve on the concepts of natural and violent motion—without much success.

Then, in the early seventeenth century, Italian astronomer and physicist Galileo Galilei (1564–1642) proposed a whole new way of looking at the problem of motion. Since asking why things move had not been very productive, Galileo said, perhaps physicists should focus simply on describing how they move. A whole new philosophy of physics (the science of matter and energy) was created and, in the process, the science of physics itself was born.

Newton's three laws

Newton, who was born in the year that Galileo died, produced a nearly perfect (for the time) response to Galileo's suggestion. He said that the movement of objects can be fully described in only three laws. These laws all show how motion is related to forces. One definition for the term force in science is a push or a pull. If you push a wooden block across the top of a table, for example, you exert a force on the block. One benefit of Newton's laws is that they provide an even more precise definition for force, as will be demonstrated later.

The first law. Newton's first law of motion is that an object tends to continue in its motion at a constant velocity until and unless an outside force acts on it. The term velocity refers both to the speed and the direction in which an object is moving.

For example, suppose that you shoot an arrow into space. Newton's first law says that the arrow will continue moving in the direction you aimed it at its original speed until and unless some outside force acts on it. The main outside forces acting on an arrow are friction from air and gravity.

Words to Know

Acceleration: The rate at which the velocity of an object changes with time.

Force: A physical interaction (pushing or pulling) tending to change the state of motion (velocity) of an object.

Inertia: The tendency of an object to continue in its state of motion.

Mass: A measure of an amount of matter.

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

As the arrow continues to move, it will slow down. The arrow is passing through air, whose molecules rub against the arrow, causing it to lose speed. In addition, the arrow begins to change direction, moving toward Earth because of gravitational forces. If you could imagine shooting an arrow into the near-perfect vacuum of outer space, the arrow would continue moving in the same direction at the same speed forever. With no air present—and beyond the range of Earth's gravitational attraction—the arrow's motion would not change.

The first law also applies to objects at rest. An object at rest is simply an object whose velocity is zero. The object will continue to remain at rest until and unless a force acts on it. For example, a person might hit the object with a mallet. The force of the blow might change the object's motion, giving it both speed and direction.

The property of objects described by the first law is known as inertia. The term inertia simply means that objects tend to continue in whatever their state of motion is. If moving, they continue to move in the same way, or, if at rest, they continue to remain at rest unless acted on by an outside force.

The second law. Newton's second law clearly states the relationship between motion and force. Mathematically, the law can be stated as F = m · a, where F represents the force exerted on an object, m is the object's mass, and a is the acceleration given to the object. The term acceleration means how fast the velocity of an object is changing and in what direction.

To understand the second law, think of a soccer ball sitting on the ground. If you kick that ball with a certain force, the ball will be given a certain acceleration. If you kick the ball with twice the force, the ball will be given twice the acceleration. If the ball then bounces off the goal post and out of bounds, the force of the impact with the goal post will change the ball's direction.

The second law provides a more precise way of defining force. Force is any action that causes a body to change the speed or direction with which it is moving.

The third law. Newton's third law says that for every action there is an equal and opposite reaction. A simple example of the law is a rocket. A rocket is simply a cylindrical device closed at one end and open at the other end in which a fuel is burned. As the fuel burns, hot gases are formed and released through the open end of the rocket. The escape of the gases in one direction can be considered as an action. Newton's law says that this action must be balanced by a second action that is equal in magnitude and opposite in direction. That opposite action is the movement of the rocket in a direction opposite that of the escaping gases. That is, the gases go out the back of the rocket (the action), while the rocket itself moves forward (the reaction).

[See also Acceleration; Celestial mechanics; Gravity and gravitation; Mass ]

Laws of motion

What makes a bird fly? A person run? A judo expert flip a heavier opponent? Earth orbit the Sun ? These and any other motions are governed by three deceptively simple laws first stated by Isaac Newton in the seventeenth century. These three laws of motion when coupled with Newton's law of gravity form the basis for explaining both the motions we see on theearth and the motions of the heavenly bodies.

History

In the sixteenth century, Copernicus suggested that Earth and other planets orbited the Sun, but his model contained no physics . It did not say why the planets should orbit the Sun. Galileo was censured by the Catholic Church and forced to recant his belief in the Copernican model. He then realized that to ultimately win the Copernican model needed a physical basis. Galileo therefore started to quietly develop the new physics needed to explain planetary motions. Isaac Newton, who was born the year Galileo died, built on the foundation laid by Galileo. The resulting edifice, Newton's laws, was a grand synthesis that for the first time explained motions both on Earth and in the heavens with a unified set of laws.

Newton's three laws

Slide a block of wood across a level uncarpeted floor and notice its behavior . The block continues to move as long as you apply a force . When the force stops, the block stops moving. The block will continue to slide for a while after you stop applying a force. Your pushing is not the only force acting on the block. There is also a frictional force opposing the motion. The block sliding across the floor stops because this frictional force acts on it. The block on an icy surface takes longer to stop because there is less frictional force. If you could slide the block across a surface with absolutely no friction , it would never stop. The block would keep moving until some outside force, such as the wall of the room, stopped it. A block on a level surface, without application of forces will not move unless something applies an outside force; it will remain there at rest forever.

The first of Newton's laws states an object will continue its motion at a constant velocity until an outside force acts on it. The block has a tendency to continue in its state of motion, whatever that state might be, until some force changes that state of motion. This tendency to continue in a state of motion is called the object's inertia. An object at rest simply has a constant velocity of zero , so it needs an outside force to start moving. The physicist's definition of velocity includes both speed and direction, so any deviation from straight line motion is a change in velocity and will require an outside force. The inertia of any object will cause it to continue to move at a constant (in a straight line) velocity (or stay at rest) until an outside force acts on it.

A block will slide more easily than, for instance, a refrigerator because it has less mass . Newton's first law says that a force is needed to change the velocity of an object; the second law tells us how much force. Any change in velocity (speed up, slow down, or change direction) is an acceleration . For the common case where the mass does not change, Newton's second law states that the force required is equal to the accelerated mass times the acceleration (Force = Mass × Acceleration). It's harder to slide the refrigerator than the block across the floor because the greater mass requires a greater force to accelerate it from rest. A force in the same direction as the velocity increases the velocity; in the opposite direction, decreases it. A force perpendicular to the velocity changes the direction of motion. Occasionally the accelerated mass changes. In this case, the force is equal to the rate at which the momentum changes with time.

Newton's third law states that for every action there is an equal and opposite reaction. The action and reaction are equal and opposite forces forming an action reaction pair. If you are sitting in a chair, Earth's gravity pulls you down. The reaction is that you pull Earth up with exactly the same amount of force. The action reaction pair is: you on Earth, Earth on you. The reaction is NOT as is often thought the floor or chair holding you up. Not all equal and opposite forces form an action reaction pair.

Newton's three laws of motion revolutionized physics. For the first time the same simple set of laws explained a wide variety of apparently unrelated types of motion both on Earth and in the heavens. Not until the twentieth century were these laws surpassed by quantum mechanics and relativity for the special cases of subatomic particles , motion near the speed of light and strong gravitational fields.

See also Gravity and gravitation; Relativity, general.

Resources

books

Feynman, Richard P., Robert B. Leighton, and Mathew Sands. The Feynman Lectures on Physics. Vol.1. Reading, MA: Addison-Wesley, 1963.

Hewitt, Paul. Conceptual Physics. New York: Prentice Hall, 2001.

Ostdiek, Vern J., and Donald J. Bord. Inquiry into Physics. 2nd ed. St. Paul: West Publishing, 1991.

Serway, Raymond, Jerry S. Faughn, and Clement J. Moses. College Physics. 6th ed. Pacific Grove, CA: Brooks/Cole, 2002.

Paul A. Heckert

KEY TERMS

Acceleration

—The rate at which the velocity of an object changes over time.

Force

—Influence exerted on an object by an outside agent which produces an acceleration changing the object's state of motion.

Inertia

—The tendency of an object in motion to remain in motion, and the tendency of an object at rest to remain at rest.

Mass

—A measure of the amount of matter in kilograms. Related both to the resistance to the change in motion and to the amount of gravitational force.

Velocity

—The speed and direction of a moving object.