Write down application of Newton third …

Isaac Newton’s calculus actually began in 1665 with his discovery of the general binomial series(1 + x)n = 1 + nx + n(n − 1)/2!∙x2 + n(n − 1)(n − 2)/3!∙x3 +⋯for arbitrary rational values of n. With this formula he was able to find infinite series for many algebraic functions (functions y of x that satisfy a polynomial equation p(x, y) = 0). For example,(1 + x)−1 = 1 − x + x2 − x3 + x4 − x5 +⋯ and1/Square root of√(1 − x2) = (1 + (−x2))−1/2 = 1 + 1/2∙x2 + 1∙3/2∙4∙x4+1∙3∙5/2∙4∙6∙x6 +⋯. In turn, this led Newton to infinite series for integrals of algebraic functions. For example, he obtained the logarithm by integrating the powers of x in the series for (1 + x)−1 one by one,log (1 + x) = x − x2/2 + x3/3 − x4/4 + x5/5 − x6/6 +⋯,and the inverse sine series by integrating the series for 1/Square root of√(1 − x2),sin−1(x) = x + 1/2∙x3/3 + 1∙3/2∙4∙x5/5 + 1∙3∙5/2∙4∙6∙x7/7 +⋯. Finally, Newton crowned this virtuoso performance by calculating the inverse series for x as a series in powers of y = log (x) and y = sin−1 (x), respectively, finding the exponential seriesx = 1 + y/1! + y2/2! + y3/3! + y4/4! +⋯and the sine seriesx = y − y3/3! + y5/5! − y7/7! +⋯. Note that the only differentiation and integration Newton needed were for powers of x, and the real work involved algebraic calculation with infinite series. Indeed, Newton saw calculus as the algebraic analogue of arithmetic with infinite decimals, and he wrote in his Tractatus de Methodis Serierum et Fluxionum (1671; “Treatise on the Method of Series and Fluxions”): Get a Britannica Premium subscription and gain access to exclusive content.Subscribe Now I am amazed that it has occurred to no one (if you except N. Mercator and his quadrature of the hyperbola) to fit the doctrine recently established for decimal numbers to variables, especially since the way is then open to more striking consequences. For since this doctrine in species has the same relationship to Algebra that the doctrine of decimal numbers has to common Arithmetic, its operations of Addition, Subtraction, Multiplication, Division and Root extraction may be easily learnt from the latter’s. For Newton, such computations were the epitome of calculus. They may be found in his De Methodis and the manuscript De Analysi per Aequationes Numero Terminorum Infinitas (1669; “On Analysis by Equations with an Infinite Number of Terms”), which he was stung into writing after his logarithmic series was rediscovered and published by Nicolaus Mercator. Newton never finished the De Methodis, and, despite the enthusiasm of the few whom he allowed to read De Analysi, he withheld it from publication until 1711. This, of course, only hurt him in his priority dispute with Gottfried Wilhelm Leibniz. John Colin Stillwell Learn More in these related Britannica articles:  Isaac Newton Isaac Newton, English physicist and mathematician, who was the culminating figure of the...…  binomial theorem Binomial theorem, statement that for any positive integer n, the nth power...…  Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz, German philosopher, mathematician, and political adviser, important...…  HISTORY AT YOUR FINGERTIPS Sign up here to see what happened On This Day, every day in your inbox! Email address By signing up, you agree to our Privacy Notice.

Newton’s first law: the law of inertia Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. In fact, in classical Newtonian mechanics, there is no important distinction between rest and uniform motion in a straight line; they may be regarded as the same state of motion seen by different observers, one moving at the same velocity as the particle and the other moving at constant velocity with respect to the particle. This postulate is known as the law of inertia.  basketball; Newton's laws of motion When a basketball player shoots a jump shot, the ball always follows an arcing path. The ball follows this path because its motion obeys Isaac Newton's laws of motion. © Mark Herreid/Shutterstock.com The law of inertia was first formulated by Galileo Galilei for horizontal motion on Earth and was later generalized by René Descartes. Although the principle of inertia is the starting point and the fundamental assumption of classical mechanics, it is less than intuitively obvious to the untrained eye. In Aristotelian mechanics and in ordinary experience, objects that are not being pushed tend to come to rest. The law of inertia was deduced by Galileo from his experiments with balls rolling down inclined planes. For Galileo, the principle of inertia was fundamental to his central scientific task: he had to explain how is it possible that if Earth is really spinning on its axis and orbiting the Sun, we do not sense that motion. The principle of inertia helps to provide the answer: since we are in motion together with Earth and our natural tendency is to retain that motion, Earth appears to us to be at rest. Thus, the principle of inertia, far from being a statement of the obvious, was once a central issue of scientific contention. By the time Newton had sorted out all the details, it was possible to accurately account for the small deviations from this picture caused by the fact that the motion of Earth’s surface is not uniform motion in a straight line (the effects of rotational motion are discussed below). In the Newtonian formulation, the common observation that bodies that are not pushed tend to come to rest is attributed to the fact that they have unbalanced forces acting on them, such as friction and air resistance. Get a Britannica Premium subscription and gain access to exclusive content.Subscribe Now Newton’s second law: F = ma  Learn how immovable objects and unstoppable forces are the same A lesson proving immovable objects and unstoppable forces are one and the same. © MinutePhysics (A Britannica Publishing Partner)See all videos for this article Newton’s second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it. The momentum of a body is equal to the product of its mass and its velocity. Momentum, like velocity, is a vector quantity, having both magnitude and direction. A force applied to a body can change the magnitude of the momentum or its direction or both. Newton’s second law is one of the most important in all of physics. For a body whose mass m is constant, it can be written in the form F = ma, where F (force) and a (acceleration) are both vector quantities. If a body has a net force acting on it, it is accelerated in accordance with the equation. Conversely, if a body is not accelerated, there is no net force acting on it. Newton’s third law: the law of action and reaction Newton’s third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. The third law is also known as the law of action and reaction. This law is important in analyzing problems of static equilibrium, where all forces are balanced, but it also applies to bodies in uniform or accelerated motion. The forces it describes are real ones, not mere bookkeeping devices. For example, a book resting on a table applies a downward force equal to its weight on the table. According to the third law, the table applies an equal and opposite force to the book. This force occurs because the weight of the book causes the table to deform slightly so that it pushes back on the book like a coiled spring. If a body has a net force acting on it, it undergoes accelerated motion in accordance with the second law. If there is no net force acting on a body, either because there are no forces at all or because all forces are precisely balanced by contrary forces, the body does not accelerate and may be said to be in equilibrium. Conversely, a body that is observed not to be accelerated may be deduced to have no net force acting on it. Influence of Newton’s laws Newton’s laws first appeared in his masterpiece, Philosophiae Naturalis Principia Mathematica (1687), commonly known as the Principia. In 1543 Nicolaus Copernicus suggested that the Sun, rather than Earth, might be at the centre of the universe. In the intervening years Galileo, Johannes Kepler, and Descartes laid the foundations of a new science that would both replace the Aristotelian worldview, inherited from the ancient Greeks, and explain the workings of a heliocentric universe. In the Principia Newton created that new science. He developed his three laws in order to explain why the orbits of the planets are ellipses rather than circles, at which he succeeded, but it turned out that he explained much more. The series of events from Copernicus to Newton is known collectively as the Scientific Revolution. In the 20th century Newton’s laws were replaced by quantum mechanics and relativity as the most fundamental laws of physics. Nevertheless, Newton’s laws continue to give an accurate account of nature, except for very small bodies such as electrons or for bodies moving close to the speed of light. Quantum mechanics and relativity reduce to Newton’s laws for larger bodies or for bodies moving more slowly. The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by Erik Gregersen, Senior Editor. Learn More in these related Britannica articles:  mechanics: Newton’s laws of motion and equilibrium In his Principia, Newton reduced the basic principles of mechanics to three laws:…  celestial mechanics: Newton’s laws of motion The empirical laws of Kepler describe planetary motion, but Kepler made no attempt to define or constrain...…  evolution: Genetic equilibrium: the Hardy-Weinberg law …role similar to that of Newton’s first law of motion in mechanics. Newton’s first law says that a body...…  HISTORY AT YOUR FINGERTIPS Sign up here to see what happened On This Day, every day in your inbox! Email address By signing up, you agree to our Privacy Notice. NEWTON AND INFINITE SERIES Sections HomeLiteratureLibraries & Reference Works Newton and Infinite Series Cite Share More BY John Colin Stillwell View Edit History Isaac Newton’s calculus actually began in 1665 with his discovery of the general binomial series(1 + x)n = 1 + nx + n(n − 1)/2!∙x2 + n(n − 1)(n − 2)/3!∙x3 +⋯for arbitrary rational values of n. With this formula he was able to find infinite series for many algebraic functions (functions y of x that satisfy a polynomial equation p(x, y) = 0). For example,(1 + x)−1 = 1 − x + x2 − x3 + x4 − x5 +⋯ and1/Square root of√(1 − x2) = (1 + (−x2))−1/2 = 1 + 1/2∙x2 + 1∙3/2∙4∙x4+1∙3∙5/2∙4∙6∙x6 +⋯.  In turn, this led Newton to infinite series for integrals of algebraic functions. For example, he obtained the logarithm by integrating the powers of x in the series for (1 + x)−1 one by one,log (1 + x) = x − x2/2 + x3/3 − x4/4 + x5/5 − x6/6 +⋯,and the inverse sine series by integrating the series for 1/Square root of√(1 − x2),sin−1(x) = x + 1/2∙x3/3 + 1∙3/2∙4∙x5/5 + 1∙3∙5/2∙4∙6∙x7/7 +⋯. Finally, Newton crowned this virtuoso performance by calculating the inverse series for x as a series in powers of y = log (x) and y = sin−1 (x), respectively, finding the exponential seriesx = 1 + y/1! + y2/2! + y3/3! + y4/4! +⋯and the sine seriesx = y − y3/3! + y5/5! − y7/7! +⋯. Note that the only differentiation and integration Newton needed were for powers of x, and the real work involved algebraic calculation with infinite series. Indeed, Newton saw calculus as the algebraic analogue of arithmetic with infinite decimals, and he wrote in his Tractatus de Methodis Serierum et Fluxionum (1671; “Treatise on the Method of Series and Fluxions”): Get a Britannica Premium subscription and gain access to exclusive content.Subscribe Now I am amazed that it has occurred to no one (if you except N. Mercator and his quadrature of the hyperbola) to fit the doctrine recently established for decimal numbers to variables, especially since the way is then open to more striking consequences. For since this doctrine in species has the same relationship to Algebra that the doctrine of decimal numbers has to common Arithmetic, its operations of Addition, Subtraction, Multiplication, Division and Root extraction may be easily learnt from the latter’s. For Newton, such computations were the epitome of calculus. They may be found in his De Methodis and the manuscript De Analysi per Aequationes Numero Terminorum Infinitas (1669; “On Analysis by Equations with an Infinite Number of Terms”), which he was stung into writing after his logarithmic series was rediscovered and published by Nicolaus Mercator. Newton never finished the De Methodis, and, despite the enthusiasm of the few whom he allowed to read De Analysi, he withheld it from publication until 1711. This, of course, only hurt him in his priority dispute with Gottfried Wilhelm Leibniz. John Colin Stillwell Learn More in these related Britannica articles:  Isaac Newton Isaac Newton, English physicist and mathematician, who was the culminating figure of the...…  binomial theorem Binomial theorem, statement that for any positive integer n, the nth power...…  Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz, German philosopher, mathematician, and political adviser, important...…  HISTORY AT YOUR FINGERTIPS Sign up here to see what happened On This Day, every day in your inbox! Email address By signing up, you agree to our Privacy Notice. MOTION Sections & Media HomeSciencePhysicsMatter & Energy Motion mechanics Cite Share More BY The Editors of Encyclopaedia Britannica View Edit History FULL ARTICLE Motion, in physics, change with time of the position or orientation of a body. Motion along a line or a curve is called translation. Motion that changes the orientation of a body is called rotation. In both cases all points in the body have the same velocity (directed speed) and the same acceleration (time rate of change of velocity). The most general kind of motion combines both translation and rotation. Key People:  Thomas Hobbes Galileo Gottfried Wilhelm Leibniz Jean Buridan Pafnuty ChebyshevRelated Topics: Brownian motion Wave motion Vibration Phase Action All motions are relative to some frame of reference. Saying that a body is at rest, which means that it is not in motion, merely means that it is being described with respect to a frame of reference that is moving together with the body. For example, a body on the surface of the Earth may appear to be at rest, but that is only because the observer is also on the surface of the Earth. The Earth itself, together with both the body and the observer, is moving in its orbit around the Sun and rotating on its own axis at all times. As a rule, the motions of bodies obey Newton’s laws of motion. However, motion at speeds close to the speed of light must be treated by using the theory of relativity, and the motion of very small bodies (such as electrons) must be treated by using quantum mechanics.  READ MORE ON THIS TOPIC philosophy of physics: The question of motion Long before Kant, Newton himself designed a thought experiment to show that relationism must be false.... The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by Adam Augustyn, Managing Editor, Reference Content. Learn More in these related Britannica articles:  philosophy of physics: The question of motion Long before Kant, Newton himself designed a thought experiment to show that relationism must be false....…  Aristotle: Motion Motion (kinesis) was for Aristotle a broad term, encompassing changes in several different...…  mathematics: The universities Uniformly accelerated motion starting at zero velocity gives rise to a triangular figure (see...…  HISTORY AT YOUR FINGERTIPS Sign up here to see what happened On This Day, every day in your inbox! Email address By signing up, you agree to our Privacy Notice.