+
+
+ 
+ In classical mechanics, Newton's laws of motion are three laws that describe the relationship
+ between the motion of an object and the forces acting on it. The first law states that an object
+ either remains at rest or continues to move at a constant velocity,
+ unless it is acted upon by an external force. The second law states that the rate of change
+ f momentum of an object is directly proportional to the force applied, or, for an object with
+ constant mass, that the net force on an object is equal to the mass of that object multiplied
+ by the acceleration. The third law states that when one object exerts a force on a second object,
+ that second object exerts a force that is equal in magnitude and opposite in direction on the first object.
+
+
+ The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia
+ Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687.
+ Newton used them to explain and investigate the motion of many physical objects and systems,
+ which laid the foundation for Newtonian mechanics.
+
+
+
+
+ The First Law
+ The first law states that an object at rest will stay at rest, and an object in motion will
+ stay in motion unless acted on by a net external force. Mathematically,
+ this is equivalent to saying that if the net force on an object is zero,
+ then the velocity of the object is constant.
+
+ 
+
Newton's first law is often referred to as the law of inertia.
+ Newton's first (and second) laws are valid only in an inertial reference frame.[4]
+
+
+
+ The Second Law
+ The second law states that the rate of change of momentum of a body over time is directly
+ proportional to the force applied, and occurs in the same direction as the applied force.
+
+
+
Constant Mass
+ For objects and systems with constant mass,[5][6][7] the second law can be re-stated in terms of an
+ object's
+ acceleration.
+
+
+ 
+
where F is the net force applied, m is the mass of the body, and a is the body's acceleration. Thus, the
+ net
+ force applied to a body produces a proportional acceleration.
+
+ Variable-mass systems
+
+ Variable-mass systems, like a rocket burning fuel and ejecting spent gases,
+ are not closed and cannot be directly treated by making mass a function of time in the second law;[6][7]
+ The
+ equation of motion for a body whose mass m varies with time by either ejecting or accreting mass is
+ obtained
+ by
+ applying the second law to the entire, constant-mass system consisting of the body and its ejected or
+ accreted
+ mass;
+ the result is[5]
+
+
+
where u is the exhaust velocity of the escaping or incoming mass relative to the body. From this equation
+ one
+ can derive the equation of motion for a varying mass system, for example, the Tsiolkovsky rocket equation.
+ Under some conventions, the quantity
+ 
+
on the left-hand side, which represents the advection of momentum, is defined as a force (the force exerted
+ on the body by the changing mass, such as rocket
+ exhaust) and is included in the quantity F. Then, by substituting the definition of acceleration, the
+ equation becomes F = ma.
+
+
+
+
+ The Third Law
+ The third law states that all forces between two objects exist in equal magnitude and opposite direction:
+ if
+ one
+ object A exerts a force FA on a second object B, then B simultaneously exerts a force FB on A, and the two
+ forces
+ are equal in magnitude and opposite in direction: FA = −FB.[8] The third law means that all forces are
+ interactions between different bodies,[9][10] or different regions within one body, and thus that there is
+ no
+ such
+ thing as a force that is not accompanied by an equal and opposite force. In some situations, the magnitude
+ and
+ direction of the forces are determined entirely by one of the two bodies, say Body A; the force exerted by
+ Body
+ A
+ on Body B is called the "action", and the force exerted by Body B on Body A is called the "reaction". This
+ law
+ is
+ sometimes referred to as the action-reaction law, with FA called the "action" and FB the "reaction". In
+ other
+ situations the magnitude and directions of the forces are determined jointly by both bodies and it isn't
+ necessary
+ to identify one force as the "action" and the other as the "reaction". The action and the reaction are
+ simultaneous, and it does not matter which is called the action and which is called reaction; both forces
+ are
+ part
+ of a single interaction, and neither force exists without the other.[8]
+
+ 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).
+
+ From a conceptual standpoint, Newton's third law is seen when a person walks: they push against the floor,
+ and
+ the
+ floor pushes against the person. Similarly, the tires of a car push against the road while the road pushes
+ back
+ on
+ the tires—the tires and road simultaneously push against each other. In swimming, a person interacts with
+ the
+ water, pushing the water backward, while the water simultaneously pushes the person forward—both the
+ person
+ and
+ the water push against each other. The reaction forces account for the motion in these examples. These
+ forces
+ depend on friction; a person or car on ice, for example, may be unable to exert the action force to
+ produce
+ the
+ needed reaction force.[11]
+
+ Newton used the third law to derive the law of conservation of momentum;[12] from a deeper perspective,
+ however,
+ conservation of momentum is the more fundamental idea (derived via Noether's theorem from Galilean
+ invariance),
+ and holds in cases where Newton's third law appears to fail, for instance when force fields as well as
+ particles
+ carry momentum, and in quantum mechanics.
+
+
+
+ History
+ The ancient Greek philosopher Aristotle had the view that all objects have a natural place in the
+ universe:
+ that
+ heavy objects (such as 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. He thought that a body was in its natural
+ state
+ when it was at rest, and for the body to move in a straight line at a constant speed an external agent was
+ needed
+ continually to propel it, otherwise it would stop moving. Galileo Galilei, however, realised that a force
+ is
+ necessary to change the velocity of a body, i.e., acceleration, but no force is needed to maintain its
+ velocity.
+ In other words, Galileo stated that, in the absence of a force, a moving object will continue moving. (The
+ tendency of objects to resist changes in motion was what Johannes Kepler had called inertia.) This insight
+ was
+ refined by Newton, who made it into his first law, also known as the "law of inertia"—no force means no
+ acceleration, and hence the body will maintain its velocity. As Newton's first law is a restatement of the
+ law
+ of
+ inertia which Galileo had already described, Newton appropriately gave credit to Galileo.
+
+
+ Links
+
+
+ - Browne, Michael E. (July 1999). Schaum's outline of theory and problems of physics for engineering
+ and
+ science (Series: Schaum's Outline Series). McGraw-Hill Companies. p. 58. ISBN 978-0-07-008498-8.
+ - the Principia on line at Andrew Motte Translation
+ - Andrew Motte translation of Newton's Principia (1687) Axioms or Laws of Motion
+ - Thornton, Marion (2004). Classical dynamics of particles and systems (5th ed.). Brooks/Cole. p. 53.
+ ISBN 978-0-534-40896-1.
+
+ - Plastino, Angel R.; Muzzio, Juan C. (1992). "On the use and abuse of Newton's second law for
+ variable
+ mass problems". Celestial Mechanics and Dynamical Astronomy. 53 (3): 227–232.
+ Bibcode:1992CeMDA..53..227P.
+ doi:10.1007/BF00052611. ISSN 0923-2958. S2CID 122212239. "We may conclude emphasizing that Newton's
+ second
+ law is valid for constant mass only. When the mass varies due to accretion or ablation, [an alternate
+ equation explicitly accounting for the changing mass] should be used."
+ - Halliday; Resnick. Physics. 1. p. 199. ISBN 978-0-471-03710-1. It is important to note that we
+ cannot
+ derive a general expression for Newton's second law for variable mass systems by treating the mass in
+ F =
+ dP/dt = d(M v) as a variable. [...] We can use F = dP/dt to analyze variable mass systems only if we
+ apply
+ it to an entire system of constant mass, having parts among which there is an interchange of mass.
+ [Emphasis as in the original]
+ - Kleppner, Daniel; Kolenkow, Robert (1973). An Introduction to Mechanics. McGraw-Hill. pp. 133–134.
+ ISBN
+ 978-0-07-035048-9 – via archive.org. Recall that F = dP/dt was established for a system composed of a
+ certain set of particles[. ... I]t is essential to deal with the same set of particles throughout the
+ time
+ interval[. ...] Consequently, the mass of the system can not change during the time of interest.
+ - Resnick; Halliday; Krane (1992). Physics, Volume 1 (4th ed.). p. 83.
+ - C Hellingman (1992). "Newton's third law revisited". Phys. Educ. 27 (2): 112–115.
+ - Resnick & Halliday (1977). Physics (Third ed.). John Wiley & Sons. pp. 78–79. Any single force is
+ only
+ one aspect of a mutual interaction between two bodies.
+ - Hewitt (2006), p. 75
+ - Newton, Principia, Corollary III to the laws of motion
+
+
+
+
+
+
+
+
+