Newton's Laws of Motion are three physical laws which provide relationships between the forces acting on a body and the motion of the body, first formulated by Sir Isaac Newton. Newton's laws were first published in his work Philosophiae Naturalis Principia Mathematica (1687). The laws form the basis for classical mechanics. Newton used them to explain many results concerning the motion of physical objects. In the third volume of the text, he showed that the laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.
Contents
1 The Three Laws of Motion
2 Newton's first law: law of inertia
3 Newton's second law: law of acceleration
4 Newton's third law: law of reciprocal actions
5 Importance and range of validity
6 Relationship to the conservation laws
7 See also
8 References
9 External links
The Three Laws of Motion
Newton's Laws of Motion describe only motion of a body as a whole and are valid only for motions relative to a reference frame. The following are brief modern formulations of Newton's three laws of motion:
First Law
A body at rest remains at rest, and a body in motion continues to move in a straight line with a constant speed unless and until an external unbalanced force acts upon it.
Second Law
The rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction in which the force acts.
Third Law
To every action (force applied) there is an equal and opposite reaction (equal force in the opposite direction).
Another way of stating Newton's third law is that if object A exerts a force on object B, then object B exerts a force of the same magnitude on A, in the opposite direction.
It is important to note that these three laws together with his law of gravitation provide a satisfactory basis for the explanation of motion of everyday macroscopic objects under everyday conditions. However, when applied to extremely high speeds or extremely small objects, Newton's laws break down; this was remedied by Albert Einstein's Special Theory of Relativity for high speeds and by quantum mechanics for small objects.
[edit] Newton's first law: law of inertia
Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.
An object at rest will remain at rest unless acted upon by an external and unbalanced force. An object in motion will remain in motion unless acted upon by an external and unbalanced force.
This law is also called the law of inertia.
The net force on an object is the vector sum of all the forces acting on the object. Newton's first law says that if this sum is zero, the state of motion of the object does not change. Essentially, it makes the following two points:
An object that is not moving will not move until a net force acts upon it.
An object that is in motion will not change velocity (accelerate) until a net force acts upon it.
The first point seems relatively obvious to most people, but the second may take some thinking through, because we have no experience in every-day life of things that keep moving forever (except celestial bodies). If one slides a hockey puck along a table, it doesn't move forever, it slows and eventually comes to a stop. But according to Newton's laws, this is because a force is acting on the hockey puck and, sure enough, there is frictional force between the table and the puck, and that frictional force is in the direction opposite the movement. It is this force which causes the object to slow to a stop. In the absence of such a force, as approximated by an air hockey table or ice rink, the puck's motion would not slow. Newton's first law is just a restatement of what Galileo had already described and Newton gave credit to Galileo. It differs from Aristotle's view that all objects have a natural place in the universe. Aristotle believed that heavy objects like rocks wanted to be at rest on the Earth and that light objects like smoke wanted to be at rest in the sky and the stars wanted to remain in the heavens.
However, a key difference between Galileo's idea from Aristotle's is that Galileo realized that force acting on a body determines acceleration, not velocity. This insight leads to Newton's First Law - no force means no acceleration, and hence the body will continue to maintain its velocity.
The Law of Inertia apparently occurred to many different natural philosophers independently. Inertia of motion was described in the third century BCE in the Mo Tzu, a collection of Chinese philosophical texts, and the 17th century philosopher René Descartes also formulated the law, although he did not perform any experiments to confirm it.
There are no perfect demonstrations of the law, as friction usually causes a force to act on a moving body, and even in outer space gravitational forces act and cannot be shielded against, but the law serves to emphasize the elementary causes of changes in an object's state of motion: forces.
[edit] Newton's second law: law of acceleration
Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.
The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction.
In an exact original 1792 translation (from Latin) Newton's Second Law of Motion reads:
LAW II: The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. — If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.
Here Newton is saying that the rate of change in the momentum of an object is directly proportional to the amount of force exerted upon the object. He also states that the change in direction of momentum is determined by the angle from which the force is applied.
However, it must be remembered that for Newton, mass was constant and independent of velocity. To take "motion" (motu) as meaning momentum gives a false impression of what Newton believed. Since he took mass as constant (part of the constant of proportionality) it can, in modern notation, be taken to the left of the derivative as . If m is dependent on velocity (and thus indirectly upon time) as we would now hold, then m has to be included in the derivative, giving or .
Using momentum in the terminology (which would never have occurred to Newton) is a latter-day revision of the law to bring it into correspondence with special relativity.
Interestingly, Newton is restating in his further explanation another prior idea of Galileo, what we call today the Galilean transformation or the addition of velocities.
An interesting fact when studying Newton's Laws of Motion from the Principia is that Newton himself does not explicitly write formulae for his laws which was common in scientific writings of that time period. In fact, it is today commonly added when stating Newton's second law that Newton has said, "and inversely proportional to the mass of the object." This however is not found in Newton's second law as directly translated above. In fact, the idea of mass is not introduced until the third law.
In mathematical terms, the differential equation can be written as:
where is force, is mass, is velocity, is time and is the constant of proportionality. The product of the mass and velocity is the momentum of the object.
If mass of an object in question is known to be constant and using the definition of acceleration, this differential equation can be rewritten as:
where is the acceleration.
Using only SI Units for the definition of Newton, the constant of proportionality is unity (1). Hence:
However, it has been a common convention to describe Newton's second law in the mathematical formula where is Force, is acceleration and is mass. This is actually a combination of laws two and three of Newton expressed in a very useful form. This formula in this form did not even begin to be used until the 18th century, after Newton's death, but it is implicit in his laws.
Newton's Third Law of Motion states:
LAW III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. -- Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone, as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinge upon another, and by its force change the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, toward the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of the bodies; that is to say, if the bodies are not hindered by any other impediments. For, because the motions are equally changed, the changes of the velocities made toward contrary parts are reciprocally proportional to the bodies. This law takes place also in attractions, as will be proved in the next scholium.
The explanation of mass is expressed here for the first time in the words "reciprocally proportional to the bodies" which have now been traditionally added to Law 2 as "inversely proportional to the mass of the object." This is because Newton in his definition 1 had already stated that when he said "body" he meant "mass". Thus we arrive at . When the formula is taken into account, Law II can be also interpreted as a quantitative restatement of Law I, where mass also acts as a measurement of inertia.
All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction.
This law of motion is most commonly paraphrased as: "For every action force there is an equal, but opposite, reaction force."
The third law follows mathematically from the law of conservation of momentum.
As shown in the diagram opposite, the skaters' forces on each other are equal in magnitude, and opposite in direction. Although the forces are equal, the accelerations are not: the less massive skater will have a greater acceleration due to Newton's second law. It is important to note that the action/reaction pair act on different objects and do not cancel each other out.
If a basketball hits the ground, the basketball's force on the Earth is the same as Earth's force on the basketball. However, due to the ball's much smaller mass, Newton's second law predicts that its acceleration will be much greater than that of the Earth. Not only do planets accelerate toward stars, but stars also accelerate toward planets. If a star gravitationally attracts a planet, then the planet will gravitationally attract the star. Usually the planet is less massive than the star and thus displays greater changes in it's state of motion. Similarly, if a falling ball is pulled towards the Earth, then the reaction force is that the Earth is pulled toward the ball. We can not detect any change in the Earth's motion because it is much more massive than the ball.
The two forces in Newton's third law are of the same type, e.g., if the road exerts a forward frictional force on an accelerating car's tires, then it is also a frictional force that Newton's third law predicts for the tires pushing backward on the road.
[edit] Importance and range of validity
Newton's laws were verified by experiment and observation for over 200 years, and they are excellent approximations at the scales and speeds of everyday life. Newton's laws of motion, together with his law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena.
According to Einstein's theory of relativity, there is no preferred frame of reference. The laws of physics are equally valid in all frames of reference. Motion can only be measured relative to a frame of reference. According to the equivalence principle, an observer on the surface of the Earth could not find any difference (in the first order) between the gravitational attraction of earth and the inertial force that he feels when he is in a rocket in outer space that accelerates upwards (from the standpoint of the observer) at 9.8 m/s2. In other words, he may regard any inertial force as a gravitational force. Consequently, Newton's laws of motion are only valid in an inertial frame of reference. Notice that the surface of the Earth does not define an inertial frame of reference because it is rotating and orbiting and because of Earth's gravity. However, since the speed of rotation and revolution change relatively slowly, the inertial force is tiny. Therefore, Newton's laws of motion remain a good approximation on earth. In a non-inertial frame of reference, inertial forces must be considered for Newton's laws to remain valid.
In quantum mechanics concepts such as force, momentum, and position are defined by linear operators that operate on the quantum state; at speeds that are much lower than the speed of light, Newton's laws are just as exact for these operators as they are for classical objects. At speeds comparable to the speed of light, the second law holds in the original form F = dp / dt, which says that the force is the derivative of the momentum of the object with respect to time, but some of the newer versions of the second law (such as the constant mass approximation above) do not hold at relativistic velocities.
To sum it up in an easy way to remember, Newton’s third law of motion can be defined as follows: (For every action there is a reaction equal in magnitude and opposite in direction)
[edit] Relationship to the conservation laws
The laws of conservation of momentum, energy, and angular momentum are of more general validity than Newton's laws, since they apply to both light and matter, and to both classical and non-classical physics.
Because force is the time derivative of momentum, the concept of force is redundant and subordinate to the conservation of momentum, and is not used in fundamental theories (e.g. quantum mechanics, quantum electrodynamics, general relativity, etc.). The standard model explains in detail how the three fundamental forces known as gauge forces originate out of exchange by virtual particles. Other forces such as gravity and fermionic degeneracy pressure arise from conditions in the equations of motion in the underlying theories.
Newton stated the third law within a world-view that assumed instantaneous action at a distance between material particles. However, he was prepared for philosophical criticism of this action at a distance, and it was in this context that he stated the famous phrase "I frame no hypotheses". In modern physics, action at a distance has been completely eliminated. For example, the electrons in the antenna of a radio transmitter do not necessarily act directly on the electrons in the receiver's antenna. According to an everyday timelike observer, momentum is handed off from the transmitter's electrons to the radio wave, and then to the receiver's electrons, and the whole process takes time. If the radio wave itself were to carry a stopwatch and a meterstick and find how long it takes for the momentum to be transferred and whether there is space between the two electrons, then from that perspective the transmitting electron acts directly and instantly on the receiving electron. Conservation of momentum is satisfied at all times and Newton's laws are applicable: for example, the second law does apply to the radio wave (see radiation pressure, radiation reaction force, etc.). Its applicability is guaranteed by accounting for radiowave momentum (see momentum of electromagnetic wave).
Conservation of energy was discovered nearly two centuries after Newton's lifetime, the long delay occurring because of the difficulty in understanding the role of microscopic and invisible forms of energy such as heat and infra-red light.
[edit] See also
Scientific laws named after people
Mercury, orbit of
Galilean invariance
General relativity
Modified Newtonian dynamics
Lagrangian mechanics
Principle of least action
References
Marion, Jerry and Thornton, Stephen. Classical Dynamics of Particles and Systems. Harcourt College Publishers, 1995. ISBN 0-03-097302-3
Fowles, G. R. and Cassiday, G. L. Analytical Mechanics (6ed). Saunders College Publishing, 1999. ISBN 0-03-022317-2
[edit] External links
Science aid: Newton's laws of motion
Newtonian Physics - an on-line textbook
Motion Mountain - an on-line textbook
Trajectory Video - video clip showing exchange of momentum
Newtonian attraction for three Planets (Mathcad Application Server)
Gravity - Newton's Law for Kids
Simulation on Newton's first law of motion
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