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Encyclopedia > Newton's Third Law

Newton's laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. These laws are fundamental to classical mechanics. This is a list of physical laws discovered by science. ... Sir Isaac Newton in Knellers 1689 portrait Sir Isaac Newton (25 December 1642 – 20 March 1727 by the Julian calendar in use in England at the time; or 4 January 1643 – 31 March 1727 by the Gregorian calendar) was an English physicist, mathematician, astronomer, philosopher, and alchemist who wrote... This article is about motion in physics. ... In physics, Classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the motions of bodies, and the forces that cause them. ...


Newton first published these laws in Philosophiae Naturalis Principia Mathematica (1687) and used them to prove many results concerning the motion of physical objects. In the third volume (of the text), he showed how, combined with his law of universal gravitation, the laws of motion would explain Kepler's laws of planetary motion. Newtons own copy of his Principia, with hand written corrections for the second edition. ... Events March 19 - The men under explorer Robert Cavelier de La Salle murder him while searching for the mouth of the Mississippi River. ... The law of universal gravitation states that gravitational force between masses decreases with the distance between them, according to an inverse-square law. ... Johannes Keplers primary contributions to astronomy/astrophysics were the three laws of planetary motion. ...

Note:In this article, vector quantities are written in bold whereas scalar ones are in italics.
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In physics and engineering, the word vector typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a magnitude and a direction. The word vector is also now used for more general concepts (see also vector and generalizations below), but this... The concept of a scalar is used in mathematics, physics, and computing. ...

Importance of Newton's laws of motion

Nature and Nature's laws lay hid in night;
God said, Let Newton be! And all was light.Alexander Pope

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 such as: the motion of spinning bodies, motion of bodies in fluids; projectiles; motion on an inclined plane; motion of a pendulum; the tides; the orbits of the Moon and the planets. The law of conservation of momentum, which Newton derived as a corollary of his second and third laws, was the first conservation law to be discovered. Alexander Pope Alexander Pope (May 22, 1688 – May 30, 1744) is considered one of the greatest English poets of the eighteenth century. ... Gravitation is the tendency of masses to move toward each other. ... For other uses of the term calculus see calculus (disambiguation) Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas. ... A subset of the phases of matter, fluids include liquids, gases, plasmas and, to some extent, plastic solids. ... A projectile is any object sent through the air by the application of some force. ... This article deals with the physical structure, not a canal inclined plane. ... A gravity pendulum is a weight on the end of a rigid rod, which, when given some initial lift from the vertical position, will swing back and forth under the influence of gravity over its central (lowest) point. ... The tide is the regular rising and falling of the oceans surface caused by changes in gravitational forces external to the Earth. ... Crust composition Oxygen 43% Silicon 21% Aluminium 10% Calcium 9% Iron 9% Magnesium 5% Titanium 2% Nickel 0. ... A planet (from the Greek πλανήτης, planētēs which means wanderer or more forcefully vagrant, tramp) is a body of considerable mass that orbits a star and that produces no energy through nuclear fusion. ... In physics, momentum is a physical quantity related to the velocity and mass of an object. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ...


Newton's laws were verified by experiment and observation for over 200 years. They describe the kinematics of the world on our scale (from 10e-6 m to 10e4, at speeds ranging from 0 to 100 000 000 m/s) beyond what can be accurately measured. In physics, kinematics is the branch of mechanics concerned with the motions of objects without being concerned with the forces that cause the motion. ...


As a rule of thumb, Newton's Laws apply for any speed up to a third of the speed of light, after which point the error becomes too big to be ignored (see Einstein's correction factor).


Newton's First Law: Law of Inertia

This law is also called the Law of Inertia or Galileo's Principle. Inertia is the tendency of any state of affairs to persist in the absence of external influences. ... This article is in need of attention. ...


Alternative formulations:

  • Every body's center of mass continues in its state of rest, or of uniform motion in a right [straight] line, unless it is compelled to change that state by forces impressed upon it.
  • A body's center of mass remains at rest, or moves in a straight line (at a constant velocity, v), unless acted upon by a net outside force.

In calculus notation, this may be expressed as: The center of mass or center of inertia of an object is a point at which the objects mass can be assumed, for many purposes, to be concentrated. ... The word line apparently derives from the Latin linum, meaning flax plant from which linen is produced; at one time, a stretched linen thread was the most reliable way to determine a straight line. ... The center of mass or center of inertia of an object is a point at which the objects mass can be assumed, for many purposes, to be concentrated. ... This article is about velocity in physics. ...


Despite the fact that Newton's First Law appears to be a special case of Newton's Second Law, the First Law defines the reference frames in which the other two laws are valid. These reference frames are called inertial reference frames or Galilean reference frames, and are moving at constant velocity, that is to say, without acceleration. (Note that an object may have a constant speed and yet have a non-zero acceleration, as in the case of uniform circular motion. This means that the surface of the Earth is not an inertial reference frame, since the Earth is rotating on its axis and orbits around the Sun. However, for many experiments, the Earth's surface can safely be assumed to be inertial. The error introduced by the acceleration of the Earth's surface is minute.) A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... In physics, an inertial frame of reference, or inertial frame for short (also descibed as absolute frame of reference), is a frame of reference in which the observers move without the influence of any accelerating or decelerating force. ...


In less formal terms, Aristotle thought that things stood still if you left them alone, that to be at rest was natural, and that movement needed a cause. It would be natural to think thus, as any movement (except for that of celestial objects, which were deemed perfect) that one observes eventually stops because of friction. But Galileo's experiments, with a ball rolling down an inclined plane, found that "Things travel naturally at a steady speed (which may or may not be zero), if left alone". This article is about the resistive force. ... Galileo Galilei (Pisa, February 15, 1564 – Arcetri, January 8, 1642), was a Tuscan astronomer, philosopher, and physicist who is closely associated with the scientific revolution. ... This article deals with the physical structure, not a canal inclined plane. ...


Moving from Aristotle's "A body's natural state is at rest" to Galileo's discovery (Newton's First Law) was one of the most profound and important discoveries in physics. In everyday life, the force of friction usually acts upon moving objects, slowing them down and eventually bringing them to rest. Newton described a mathematical model from which one could derive the motions of bodies from elementary causes: forces. The Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638) was Galileos final book and a sort of scientific testament covering much of his work in physics over the preceding thirty years. ... This article is about the resistive force. ...


Newton's Second Law: Fundamental law of dynamics

Alternative formulations:

  • The rate of change in momentum is proportional to the net force acting on the object and takes place in the direction of the force.
  • The acceleration of an object of constant mass is proportional to the resultant force acting upon it.

These formulations may be expressed mathematically in the following ways: In physics, momentum is a physical quantity related to the velocity and mass of an object. ... Acceleration is the time rate of change of velocity, and at any point on a v-t graph, it is given by the gradient of the tangent to that point In physics, acceleration (symbol: a) is defined as the rate of change (or time derivative) of velocity. ... This article is about proportionality, the mathematical relation. ...

  or  if m is constant. 

where

This equation expresses that In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. ... Acceleration is the time rate of change of velocity, and at any point on a v-t graph, it is given by the gradient of the tangent to that point In physics, acceleration (symbol: a) is defined as the rate of change (or time derivative) of velocity. ... This article is about velocity in physics. ... In physics, momentum is a physical quantity related to the velocity and mass of an object. ...

  • the more net force acts on an object, the greater the change in its momentum will be.

The quantity m, or mass, in the above equation is is a characteristic of the object. For an object of constant mass m (a constant of proportionality) the more net force acts on an object, the greater the change in its acceleration will be. This equation, therefore, indirectly defines the concept of mass.


In the equation, F = ma, a is directly measurable but F is not. The second law only has meaning if we are able to assert, in advance, the value of F. Rules for calculating force include Newton's law of universal gravitation. The law of universal gravitation states that gravitational force between masses decreases with the distance between them, according to an inverse-square law. ...


But is not always valid. In general both the mass of the object and its velocity can be variable. For this case:

  

This equation works in cases when the mass is variable. This equation is also valid in special relativity if we express the momentum as , where γ is the well known . A simple introduction to this subject is provided in Special relativity for beginners Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ...


The physical meaning behind this equation is important as it implies that objects interact by exchanging momentum, and they do this via a force.


Taken together with Newton's Third Law of Motion, Newton's Second Law implies the Law of Conservation of Momentum.


Newton's Third Law: Law of reciprocal actions

Alternative formulations:

  • Whenever one body exerts force upon a second body, the second body exerts an equal and opposite force upon the first body.
  • Momentum is conserved.

The very common formulation "for every action there is an equal and opposite reaction" should be avoided, as it is, at best, ambiguous and confusing. A better formulation would be that when there exists a force acting on a body A, due to another body B, there exists also a reciprocal force, acting on body B, due to the existence of body A. In physics, momentum is a physical quantity related to the velocity and mass of an object. ...


These formulations imply that if you strike an object with a force of 200 N, then the object also strikes you (with a force of 200 N). Not only do planets accelerate toward stars; but, stars accelerate toward planets. The reaction force has the opposite direction of action, and is of the same type and magnitude as the original force. However, it doesn't necessarily "line up" in space with the action. One example of this is a force on an electric dipole due to a point charge, when the dipole points in a direction perpendicular to the line connecting the point charge and the dipole. The force on the dipole due to the point charge is perpendicular to the line connecting them, so there is a reaction force on the point charge in the opposite direction, but these two force vectors are parallel and, even when extended to a line, they never cross each other in space. The Pleiades star cluster A star is any massive gaseous body in outer space just like the Sun. ...


It is often contended that Newton's third law is incorrect when electromagnetic forces are included: if a body A exerts a force on body B, then body B will in general exert a different force on body A (the force considered is the Lorentz force, generated by electric and magnetic fields). Modern theory predicts that the electromagnetic field generated by such interactions itself transports momentum via electromagnetic radiation. Newton's third law is valid if the momentum of the field is included in the calculations. Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... In physics, the Lorentz force is the force exerted on a charged particle in an electromagnetic field. ... The article on electrical energy is located elsewhere. ... In physics, magnetism is a phenomenon by which materials exert an attractive or repulsive force on other materials. ... An electromagnetic field is composed of two related vectorial fields, the electric field and the magnetic field. ... Electromagnetic radiation or EM radiation is a combination (cross product) of oscillating electric and magnetic fields perpendicular to each other, moving through space as a wave, effectively transporting energy and momentum. ...


Also see: Physics Study Guide (http://wikibooks.org/wiki/Force_(Physics_Study_Guide))


Weak and strong forms of Newton's third law

The so-called "weak form" of Newton's Third Law applies for classical physical forces (Marion and Thorton, 1995, pp. 333-337). In a system of particles, let represent the force exerted on particle a due to particle b. The weak form requires that:

All classical physical forces satisfy this condition.


The "strong form" of Newton's Third Law requires that, in addition to being equal and opposite, the forces must be directed along the line connecting the two particles. Gravitational force satisfies the strong form, while electromagnetic forces satisfy the weak form. For an example in electrostatics where the strong form is not obeyed, consider the interaction between a point charge and a perfect dipole aligned in a direction perpendicular to the line connecting the charge and the dipole.


The weak form is a valuable mathematical abstraction, because it allows one to study concepts such as the center of mass in the presence of arbitrary forces. The center of mass or center of inertia of an object is a point at which the objects mass can be assumed, for many purposes, to be concentrated. ...


Range of validity

In 1916, Einstein's theory of relativity extended the scale to which we can make predictions. But at non-relativistic (low-enough) speeds, his relativistic model reduces to the classical one presented in this article. 1916 is a leap year starting on Saturday (link will take you to calendar) Events January-February January 1 -The first successful blood transfusion using blood that had been stored and cooled. ... Portrait of Albert Einstein taken by Yousuf Karsh on February 11, 1948 Albert Einstein (March 14, 1879 – April 18, 1955) was a theoretical physicist who is widely regarded as the greatest scientist of the 20th century. ... Albert Einsteins theory of relativity is a set of two theories in physics: special relativity and general relativity. ...



Or, put more simply, the multiplying correction factor (called γ) approaches one, for speeds less than a third of the speed of light.


See also

This is a list of scientific laws named after people. ...

References

  • Marion, Jerry and Thornton, Stephen. Classical Dynamics of Particles and Systems. Harcourt College Publishers, 1995.

 
 

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