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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no" />
<meta name="description" content="Newton's laws of motion are three laws that describe the relationship between
the motion of an object and the forces acting on it.">
<title>Newton's laws of motion</title>
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<header id="laws">
<h1>Newton's laws of motion</h1>
<nav class="one">
<ul>
<li><a href="#laws">Laws</a></li>
<li><a href="#law-1">1st law</a></li>
<li><a href="#law-2">2dn law</a></li>
<li><a href="#law-3">3rd law</a></li>
<li><a href="#history">History</a></li>
<li><a href="#links">Links</a></li>
</ul>
</nav>
</header>
<main>
<article>
<img src="https://upload.wikimedia.org/wikipedia/commons/8/83/Sir_Isaac_Newton_%281643-1727%29.jpg"
alt="Isaac Newton" height="270px">
<p>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.
</p>
<p>
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.
</p>
<hr>
</article>
<article>
<h2 id="law-1">The First Law</h2>
<p>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.</p>
<div class="math"><img
src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf29dd89fdaf777f52adebc3735e4b63d3ef8810">
</div>
<p>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]</p>
</article>
<article>
<hr>
<h2 id="law-2">The Second Law</h2>
<p>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.
<div class="math"><img
src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1738cbe14085332f1dc18499c2b47ac496cd09b4">
</div>
<h3>Constant Mass</h3>
<p>For objects and systems with constant mass,[5][6][7] the second law can be re-stated in terms of an
object's
acceleration.</p>
<div class="math"><img
src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ca4b7a15aad6089d7d5efc8c2d7366d72717b83">
</div>
<p>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.</p>
<h3>Variable-mass systems</h3>
<p>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]</p>
<div class="math"><img
src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ca4b7a15aad6089d7d5efc8c2d7366d72717b83">
</div>
<p>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</p>
<div class="math"><img
src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f230275cb3238227dff7b60d438b80ae0daa4ab">
</div>
<p>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.
</p>
</article>
<article>
<hr>
<h2 id="law-3">The Third Law</h2>
<p>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.</p>
</article>
<article>
<hr>
<h2 id="history">History</h2>
<p>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.</p>
</article>
<hr>
<h2 id="links">Links</h2>
<p>
<ol>
<li>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.</li>
<li>the Principia on line at Andrew Motte Translation</li>
<li>Andrew Motte translation of Newton's Principia (1687) Axioms or Laws of Motion </li>
<li> Thornton, Marion (2004). Classical dynamics of particles and systems (5th ed.). Brooks/Cole. p. 53.
ISBN 978-0-534-40896-1.</li>
<li>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."</li>
<li>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]</li>
<li>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.</li>
<li>Resnick; Halliday; Krane (1992). Physics, Volume 1 (4th ed.). p. 83.</li>
<li>C Hellingman (1992). "Newton's third law revisited". Phys. Educ. 27 (2): 112–115.</li>
<li>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.</li>
<li>Hewitt (2006), p. 75</li>
<li>Newton, Principia, Corollary III to the laws of motion</li>
</ol>
</p>
</main>
<footer>
<p>Artur Nikitsin (c) 2021</p>
<span><a href="https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion">Wikipedia.org</a></span>
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