█▓▒░(°TaNoLi°)░▒▓█ نیوٹن کے قوانین حرکتNewton's laws of motion

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نیوٹن کے قوانین حرکت

ایک انگریز سائنسدان سر آئزک نیوٹن نے حرکت کے تین بنیادی قوانین وضع کیے:

نیوٹن کا پہلا قانون حرکت

بیان

"کسی بھی بیرونی قوت کی غیر موجودگی میں جو جسم حالت سکون میں ہوگا وہ ساکن رہے گا اور جو جسم حالت حرکت میں ہوگا وہ اسی ولاسٹی سے خط مستقیم میں اپنی حرکت کو جاری رکھے گا۔"

نیوٹن کا دوسرا قانون حرکت

بیان

"جب کسی جسم پہ کوئ بیرونی قوت اثرانداز ھوتی ھے تو یہ قوت اپنی ھی سمت میں ایک اسراع پیدا کرتی ھے۔ یہ اسراع قوت کے راست متناسب ھوتا ھے، جب کہ جسم کی کمیت کے بالعکس متناسب ھوتا ھے۔"

کسی جسم میں پیدا شدہ اسراع a اس پر عامل قوت F کے راست متناسب ہوتا ہے، ، اور تناسب کا دائم جسم کی کمیت m ہوتا ہے، یعنی

نیوٹن کا تیسرا قانون حرکت

بیان

"ھر عمل کا برابر مگر مخالف ردعمل ھوتا ھے۔" منظوم انداز

اک جسم لگاتا ہے دوجے پہ جو اک قوت

دوجا بھی لگائے گا پہلے پہ وہی قوت

مقدار میں یکساں ہیں پر سمت مخالف ہے

اک ہے عمل کی ، دوجی ردِّ عمل کی قوت

Newton's laws of motion are three physical laws that form the basis for classical mechanics.

 

They describe the relationship

 

between the forces acting on a body and its motion due to those forces. They have been

 

expressed in several different ways over

 

nearly three centuries,[1] and can be summarized as follows:

First law:

If an object experiences no net force, then its velocity is constant: t

he object is either

 at rest (if its velocity is zero), or it 

moves in a straight line with constant speed (if its velocity is nonzero).[2][3][4]

Second law: 

The acceleration a of a body is parallel and directly proportional to the net force F

 acting on the body, is in the 

direction of the net force, and is inversely proportional to the mass m of the body, i.e., F = ma.

Third law:

When a first body exerts a force F1 on a second body, the second body 

simultaneously exerts a force F2 = −F1 on the 

first body. This means that F1 and F2 are equal in magnitude and opposite in direction.

 Newton's first law

Walter Lewin explains Newton's first law and reference frames. (MIT Course 8.01)[12]

The first law law states that if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant. Velocity is a vector quantity which expresses both the object's speed and the direction of its motion; therefore, the statement that the object's velocity is constant is a statement that both its speed and the direction of its motion are constant.

The first law can be stated mathematically as

    \sum \mathbf{F} = 0\; \Rightarrow\; \frac{\mathrm{d} \mathbf{v} }{\mathrm{d}t} = 0. 

Consequently,

    An object that is at rest will stay at rest unless an unbalanced force acts upon it.

    An object that is in motion will not change its velocity unless an unbalanced force acts upon it. This is known as uniform motion.

An object continues to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest (demonstrated when a tablecloth is skillfully whipped from under dishes on a tabletop and the dishes remain in their initial state of rest). If an object is moving, it continues to move without turning or changing its speed. This is evident in space probes that continually move in outer space. Changes in motion must be imposed against the tendency of an object to retain its state of motion. In the absence of net forces, a moving object tends to move along a straight line path indefinitely.

Newton placed the first law of motion to establish frames of reference for which the other laws are applicable. The first law of motion postulates the existence of at least one frame of reference called a Newtonian or inertial reference frame, relative to which the motion of a particle not subject to forces is a straight line at a constant speed.[9][13] Newton's first law is often referred to as the law of inertia. Thus, a condition necessary for the uniform motion of a particle relative to an inertial reference frame is that the total net force acting on it is zero. In this sense, the first law can be restated as:

    In every material universe, the motion of a particle in a preferential reference frame Φ is determined by the action of forces whose total vanished for all times when and only when the velocity of the particle is constant in Φ. That is, a particle initially at rest or in uniform motion in the preferential frame Φ continues in that state unless compelled by forces to change it.[14]

Newton's laws are valid only in an inertial reference frame. Any reference frame that is in uniform motion with respect to an inertial frame is also an inertial frame, i.e. Galilean invariance or the principle of Newtonian relativity.[15]

History

From the original Latin of Newton's Principia:

" Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare. "

Translated to English, this reads:

" Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.[16] "

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 to continually propel it, otherwise it would stop moving. Galileo Galilei, however, realized 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 Galileo 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.

The law of inertia apparently occurred to several different natural philosophers and scientists independently, including Thomas Hobbes in his Leviathan.[17] The 17th century philosopher René Descartes also formulated the law, although he did not perform any experiments to confirm it.

-- 

 Newton's second law

Walter Lewin explains Newton's second law, using gravity as an example. (MIT OCW)[18]

Explanation

The second law states that the net force on an object is equal to the rate of change (that is, the derivative) of its linear momentum p in an inertial reference frame:

    \mathbf{F} = \frac{\mathrm{d}\mathbf{p}}{\mathrm{d}t} = \frac{\mathrm{d}(m\mathbf v)}{\mathrm{d}t}.

The second law can also be stated in terms of an object's acceleration. Since the law is valid only for constant-mass systems,[19][20][21] the mass can be taken outside the differentiation operator by the constant factor rule in differentiation. Thus,

    \mathbf{F} = m\,\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t} = m\mathbf{a},

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. In other words, if a body is accelerating, then there is a force on it.

Consistent with the first law, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude; such is the case with uniform circular motion. The relationship also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum.

Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (see below).

Newton's second law requires modification if the effects of special relativity are to be taken into account, because at high speeds the approximation that momentum is the product of rest mass and velocity is not accurate.

Impulse

An impulse J occurs when a force F acts over an interval of time Δt, and it is given by

    \mathbf{J} = \int_{\Delta t} \mathbf F \,\mathrm{d}t .

Since force is the time derivative of momentum, it follows that

    \mathbf{J} = \Delta\mathbf{p} = m\Delta\mathbf{v}.

This relation between impulse and momentum is closer to Newton's wording of the second law.[24]

Impulse is a concept frequently used in the analysis of collisions and impacts.[25]

Variable-mass systems

Main article: Variable-mass system

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.[20] The reasoning, given in An Introduction to Mechanics by Kleppner and Kolenkow and other modern texts, is that Newton's second law applies fundamentally to particles.[21] In classical mechanics, particles by definition have constant mass. In case of a well-defined system of particles, Newton's law can be extended by summing over all the particles in the system:

    \mathbf{F}_{\mathrm{net}} = M\mathbf{a}_\mathrm{cm}

where Fnet is the total external force on the system, M is the total mass of the system, and acm is the acceleration of the center of mass of the system.

Variable-mass systems like a rocket or a leaking bucket cannot usually be treated as a system of particles, and thus Newton's second law cannot be applied directly. Instead, the general equation of motion for a body whose mass m varies with time by either ejecting or accreting mass is obtained by rearranging the second law and adding a term to account for the momentum carried by mass entering or leaving the system:[19]

    \mathbf F + \mathbf{u} \frac{\mathrm{d} m}{\mathrm{d}t} = m {\mathrm{d} \mathbf v \over \mathrm{d}t}

where u is the relative velocity of the escaping or incoming mass with respect to the center of mass of the body. Under some conventions, the quantity u dm/dt on the left-hand side, known as the thrust, 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

    \mathbf F = m \mathbf a.

History

Newton's original Latin reads:

" Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur. "

This was translated quite closely in Motte's 1729 translation as:

" Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd. "

According to modern ideas of how Newton was using his terminology,[26] this is understood, in modern terms, as an equivalent of:

    The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.

Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading:

    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.

The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively discussed by historians of science, along with the relations between Newton's formulation and modern formulations.[27]

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