## What Are Laws of Motion?## Using Newton's principles of motionThe basis of classical mechanics is laid out in three assertions known as Newton's laws of motion, which were first articulated by English scientist and mathematician Isaac Newton. These laws describe the relationships between forces acting on a body and its motion. ## First law of Newton: the law of inertiaAccording to Newton's first law, if a body is at rest or travelling in a straight line at a constant speed, it will continue to move at that speed or stay at rest unless acted with by a force. In fact, according to classical Newtonian mechanics, there is no significant difference between being at rest and moving uniformly in a straight line; they can both be thought of as states of motion experienced by different observers, one of whom moves at the same speed as the particle and the other of who moves at a constant speed in relation to the particle. The law of inertia is the name given to this premise. Galileo Galilei initially proposed the law of inertia for Earth's horizontal motion, and René Descartes later generalized it. Although the fundamental premise and starting point of classical mechanics is the notion of inertia, the untrained eye finds it to be less than immediately clear. In both everyday life and Aristotelian mechanics, things that are not being pushed tend to come to rest. Galileo derived the law of inertia from his studies involving balls rolling down inclined surfaces. Galileo had to explain how it was conceivable that, if the Earth is indeed rotating on its axis and circling the Sun, we do not perceive that motion. To achieve this, he had to explain the concept of inertia, which was essential to his main scientific mission. The response is supported by the concept of inertia, which states that because we move with the Earth and have a propensity to keep moving, Earth appears to be at rest to us. As a result, the concept of inertia was once a major topic of debate in science and was far from being a statement of the obvious. By the time Newton had worked out all the details, it was feasible to correctly account for the minor departures from this image brought on by the fact that the Earth's surface is not moving uniformly in a straight line (the effects of rotational motion are covered below). The frequent observation that bodies that are not pushed tend to come to rest is explained by the Newtonian formulation as the result of unbalanced forces acting on them, such friction and air resistance. ## Second law of Newton: F = maNewton's second law provides a precise explanation of the modifications that a force can make to a body's motion. According to this, a body's momentum changes at a rate that is equal to the force acting on it over time in both magnitude and direction. A body's momentum is equal to the sum of its mass and velocity. Like velocity, momentum has both a magnitude and a direction, making it a vector quantity. When a force is applied to a body, the momentum's magnitude, direction, or both can change. One of the most significant laws in all of physics is Newton's second law. F = ma, where F (force) and a (acceleration) are both vector values, can be used to represent a body whose mass m is constant. A body is accelerated according to the equation if there is a net force acting on it. On the other hand, if a body is not propelled, no net force is exerted on it. ## The law of action and response is Newton's third principle.According to Newton's third law, when two bodies come into contact, they exert forces on one another that are equal in size and directed in the opposite direction. The law of action and response is another name for the third law. This law applies to bodies in uniform or rapid motion and is crucial for analysing issues of static equilibrium, when all forces are in balance. The forces it discusses are actual phenomena, not just accounting tricks. A book laying on a table, for instance, exerts downward pressure equal to the weight of the book on the table. The third law states that the book is subject to an equal and opposing force from the table. The book is pushed back against the table like a coiled spring as a result of the table's small deformation brought on by the weight of the book. A body experiences accelerated motion in line with the second rule if there is a net force acting on it. The body does not accelerate and is considered to be in equilibrium if there is no net force acting on it, either because there are no forces at all or because all forces are exactly balanced by opposing forces. On the other hand, a body that is seen to not be moving faster can be inferred to have no net force acting on it. ## The effects of Newton's lawsPhilosophize Naturalis Principia Mathematica (1687), often known as the Principia, is considered Newton's greatest work and contains the first appearance of his laws. Instead of the Earth being at the centre of the cosmos, Nicolaus Copernicus proposed that it may be the Sun in 1543. The Aristotelian worldview, which the ancient Greeks passed down to us, would be replaced by a new science that would also explain how a heliocentric cosmos functions. In the intervening years, Galileo, Johannes Kepler, and Descartes lay the groundwork for this new science. That new science was developed by Newton in the Principia. He created his three principles to help explain why planets' orbits are ellipses rather than circles, which he was successful in doing, but it turned out that he really explained a lot more. The Scientific Revolution is the collective name for the string of occurrences from Copernicus through Newton. Quantum mechanics and relativity have during the 20th century superseded Newton's rules as the most basic tenets of physics. Nevertheless, except for tiny entities like electrons or those travelling nearly at the speed of light, Newton's equations continue to provide a reliable explanation of nature. Newton's rules are what quantum mechanics and relativity come down to for larger or slower moving objects. ## InertiaA body's inertia is a quality that makes it resist attempts to set it in motion or, if it is already moving, to change the speed or direction of it. A body's inertia is a passive characteristic that only allows it to oppose active agents like forces and torques. A moving body continues to move not because of its inertia but rather because there is no external force present to induce it to slow down, veer off course, or accelerate. The inertia of a body may be quantified in two different ways: Its resistance to the application of a force is determined by its mass, and its moment of inertia around a certain axis measures its resistance to the application of a torque at the same axis. Check out Newton's laws of motion. ## DynamicsDynamics is a subfield of mechanics and a discipline of physical science that studies how physical things move in response to the force, mass, momentum, and energy that influence them. Here is a quick explanation of dynamics. See mechanics for a comprehensive treatment. Kinematics, which explains motion in terms of position, velocity, and acceleration without regard to its causes, and kinetics, which is concerned with the impact of forces and torques on the motion of mass-bearing entities, are both subsets of dynamics. Galileo laid the groundwork for dynamics at the end of the 16th century by developing the law of motion for falling bodies through experimentation with a smooth ball rolling down an inclined plane. He was also the first to realise that force is what determines changes in a body's velocity before Isaac Newton codified this idea in his second law of motion in the 17th century. According to this equation, the force exerted on a body is proportional to the speed at which its momentum is changing. Additionally, see Newton's laws of motion. ## MechanicsMechanics is a branch of science that examines how forces affect the motion of bodies, including the unique situation where a body is at rest. The forces that bodies exert on one another are the primary issue in the problem of motion. According to the nature of the forces at play, this results in the study of subjects like gravity, electricity, and magnetism. Given the forces, one may look for the way that bodies move when subjected to those forces; this is the true domain of mechanics. History shows that one of the earliest exact disciplines to be formed was mechanics. Its underlying mathematical beauty and early extraordinary success in quantitatively explaining the motions of the Moon, Earth, and other planetary bodies had a significant impact on philosophical thinking and gave science the motivation it needed to advance in a methodical way. Statics, which deals with forces operating on and in a body at rest; kinematics, which describes the potential movements of a body or system of bodies; and kinetics, which aims to explain or predict the motion that will take place in a certain scenario, are the three disciplines of mechanics. Alternatively, mechanics can be separated based on the type of system being examined. A particle is a body that is so tiny that its shape and internal structure are irrelevant to the situation at hand, making it the simplest mechanical system. The motion of a system of two or more particles that interact with one another and may also be subject to external influences is more challenging. Three broad categories of phenomena have been used as applications for the mechanical concepts. It is possible to make extremely accurate predictions about the movements of celestial bodies like stars, planets, and satellites hundreds of years in advance. (The theory of relativity predicts certain deviations from the motion according to classical, or Newtonian, physics; but these are so minute as to be visible only with extremely precise techniques, unless in issues covering the entirety of the detectable universe or a significant fraction thereof.) In the second realm, classical mechanics accurately describes everyday objects on Earth, down to microscopic size, travelling at speeds far slower than the speed of light. Even while the forces may be quite complex and the computations lack the elegant simplicity of celestial mechanics, the engineer who constructs bridges or aeroplanes may apply the Newtonian equations of classical mechanics with confidence. The behavior of matter and electromagnetic radiation on an atomic and subatomic scale is included in the third category of phenomena. Despite some early, modest breakthroughs in characterizing the behavior of atoms in terms of classical mechanics, quantum mechanics is the right framework for handling these phenomena. ## Historical context
The study of the motions of the Sun, Moon, and the five planets that could be seen without the use of a telescope-Mercury, Venus, Mars, Jupiter, and Saturn-led to the development of celestial mechanics. The word "planet" comes from the Greek word for "wanderer," so it makes sense that some cultures would elevate these movable objects against the immovable sky to the status of gods. This status is still maintained in some ways in astrology, where the positions of the planets and Sun are believed to have some bearing on people's lives on Earth. The idea that the planets are divine and that they have an impact on human behaviour may have served as the main inspiration for thorough, ongoing monitoring of planetary motions and the creation of complex models for predicting their positions in the future. A theory of planetary motion with Earth fixed in the centre and all other planets, the Moon, and the Sun around it was postulated by the Greek astronomer Ptolemy (who resided in Alexandria circa 140 CE). The speed at which the planets move through the sky as observed from Earth varies. They occasionally even change their direction of motion, but they soon go back to the main direction. Ptolemy believed that the planets moved in an irregular manner around small circles called epicycles, with the centre of the epicyclic circle orbiting Earth on a larger circle known as a deferent. The motion's other variances were explained by slightly shifting the centroid of each planet's deferent from Earth. Ptolemy was able to forecast the motions of the planets with a high degree of precision by carefully balancing the speeds and distances. His plan was accepted as unquestionable orthodoxy and persisted for more than a millennium until the time of Copernicus. Nicolaus Copernicus believed Earth to be merely one of the planets that revolved around the Sun. He demonstrated that this model, which is heliocentric (centred on the Sun), is consistent with all evidence and is far more straightforward than Ptolemy's plan. He had to incorporate a number of epicycles to match the motions in the noncircular orbits since he believed that planetary motion had to be a combination of uniform circular motions. The epicycles were comparable to the Fourier series concepts that are currently employed to describe planetary motions. (A Fourier series is an infinite accumulation of periodic terms that smoothly fluctuate between positive and negative values, with the oscillation frequency varying from term to term. As more terms are retained, they offer increasingly better approximations to other functions.) Additionally, Copernicus calculated the relative size of his heliocentric solar system, and the results are very similar to the current calculation.
The more than 20 years of astronomical observations Tycho gathered were his biggest contribution; his measurements of the positions of the planets and stars had an unheard-of accuracy of roughly 2 arc minutes. 1/60 of a degree is equal to one arc minute. Tycho's more than 20 years of astronomical observations were his biggest contribution; they allowed him to measure the locations of the planets and stars with an unheard-of accuracy of about 2 arc minutes. A degree's 1/60th of an arc minute. ## Kepler's laws of planetary motionJohannes Kepler (1571-1630), who worked under Tycho just before he passed away, received Tycho's observations after his passing. Kepler empirically arrived at his famous three laws of planetary motion, which are: (1) the orbits of the planets are ellipses with the Sun at one focus; (2) the radial line from the Sun to the planet sweeps out equal areas in equal times; and (3) the ratio of the squares of the periods of revolution around the Sun of any two planets equals the ratio of the cubes of the semimajor axes of their resemblance. ## The investigation of gravityFor historical reasons, because Newton brought both areas to a high level of perfection, and because of its universal nature, this area of research has historically been categorized as belonging to classical mechanics. According to Newton's gravitational law, every solid particle in the universe pulls towards every other one with a force acting along the line connecting them and whose intensity is directly proportional to the product of their masses and inversely proportional to the square of their spacing. The first achievement of classical mechanics was Newton's thorough explanation of the orbits of the planets and the Moon, as well as of more subtle gravitational effects like the tides and the precession of the equinoxes (a slow, cyclical change in the direction of the Earth's axis of rotation). The fundamental concepts of rocketry and space flight can be understood without the need for additional principles, albeit of course these feats need considerable technological prowess. General theory of relativity, which Albert Einstein developed, is the name of the current gravitational theory. Einstein was intrigued by the fact that acceleration can locally annul a gravitational force (as occurs in the so-called weightlessness of astronauts in an Earth-orbiting spacecraft) and was thereby led to the concept of curved space-time from the long-known equality of the quantity "mass" in Newton's second law of motion and that in his gravitational law. Since it was finished in 1915, the theory has been admired for its mathematical elegance and ability to predict a select few occurrences, such as the gravitational bending of light around a large object. However, it has only recently emerged as a crucial area for both theoretical and experimental investigation. (Relativistic mechanics, which is not a theory of gravity, refers to Einstein's special theory of relativity.) ## The research of thermodynamics, statistical mechanics, and heatHeat is a type of internal energy connected to radiation or the erratically moving molecules that make up matter. The energy of molecular binding and rotation are not included in the definition of temperature, which is an average of a portion of the internal energy existing in a body. Absolute zero (273.15 °C or 459.67 °F) is regarded as the lowest attainable energy state for a substance. Thermal equilibrium refers to the eventual attainment of homogeneous temperature by an isolated body as well as by two or more bodies placed in touch. Thermodynamics is the formal study of states of matter at (or near) thermal equilibrium. It could analyze a wide range of thermal systems without considering their specific microstructures.
The first law of thermodynamics is the mechanics' principle of energy conservation, which is expanded to include heat and states that energy remains constant across all changes in an isolated system.
According to the second rule of thermodynamics, without the help of an outside object (like a refrigerator), heat cannot go from a region with a lower temperature to one with a higher one. The measurement of the degree of disorder among the system's constituent particles is central to the idea of entropy. A coin toss, for instance, produces a random-appearing series of heads and tails, which has a higher entropy than heads and tails that tend to cluster together. Another way to state the second law is that an isolated system's entropy never becomes lower over time.
According to the third rule of thermodynamics, the entropy is zero at absolute zero temperature, which corresponds to the state that is the most organized. ## Mathematics of statisticsBy assuming molecular chaos and using the rules of probability, statistical mechanics derives the bulk properties of systems from the mechanical properties of their molecule constituents. According to the second rule of thermodynamics, an isolated system will eventually develop to the chaotic state (the state of greatest entropy), assuming that any potential configuration of the particles is equally likely. Statistical mechanics, which can derive the rules of thermodynamics but goes beyond them by explaining fluctuations (i.e., brief departures from the thermodynamic laws that only describe average behavior), is characterized by this kind of reasoning expressed in mathematically accurate form. Brownian motion, or the random movement of tiny particles suspended in a fluid, is an illustration of a fluctuation phenomenon. Next TopicWhat is computational mechanics |