Cameron Miranda
The first scientist to propose physical laws to mathematically describe the effect of forces on the motion of bodies was Isaac Newton. Newton's three laws of motion, found in The Principia, govern how the motion of physical objects change. They define the fundamental relationship between the acceleration of an object and the forces acting upon it. Newton's first law states that an object will remain at rest or in motion unless that state is changed by an external force. This principle was first formulated by Galileo Galilei for horizontal motion on Earth and later generalized by René Descartes. Other notable scientists who have contributed to the field of physics include Huygens, James Clerk Maxwell, and Albert Einstein.
| Characteristics | Values |
|---|---|
| Name | Isaac Newton |
| Nationality | English |
| Profession | Physicist and mathematician |
| Known For | Three laws of motion |
| First Law | An object will remain at rest or in a uniform state of motion unless that state is changed by an external force |
| Second Law | Force is equal to the change in momentum (mass times velocity) over time |
| Third Law | For every action in nature, there is an equal and opposite reaction |
| Work | "Philosophiæ Naturalis Principia Mathematica" (1687); commonly known as "The Principia" |
| Influence | Influenced by Galileo Galilei and René Descartes |
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What You'll Learn
Isaac Newton's three laws of motion
The first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant speed and in a straight line, unless compelled to change by an external force. This means that if all external forces cancel each other out, there is no net force acting on the object, and it will maintain its velocity. This was a conceptual leap from the earlier belief that external forces were necessary to produce motion.
Newton's second law defines a force to be equal to the change in momentum (mass times velocity) per change in time. This means that the net force on a body is equal to the body's acceleration multiplied by its mass or the rate at which the body's momentum is changing over time.
The third law of motion states that for every action (force) in nature, there is an equal and opposite reaction. In other words, if object A exerts a force on object B, object B will also exert an equal and opposite force on object A.
Newton's laws of motion have been influential in the development of physics and have been used to investigate the motion of many physical objects and systems. They have also been applied to understand aerodynamic forces, aircraft weight, and thrust.
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Huygens' Horologium Oscillatorium
In 1673, Dutch mathematician and physicist Christiaan Huygens published a book titled 'Horologium Oscillatorium: Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae' (The Pendulum Clock: or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks). This work is regarded as one of the most important 17th-century contributions to mechanics, alongside Galileo's Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638) and Newton's Principia Mathematica (1687).
Huygens' interest in using a freely suspended pendulum to regulate clocks began in 1656, and he invented the pendulum clock in 1657. The motivation behind Horologium Oscillatorium was to address the issue of keeping accurate time, which was crucial for navigation at sea, especially for a nation heavily reliant on maritime trade like the Dutch Republic. Huygens observed that pendulums are not perfectly isochronous, with the period depending on the width of the swing. He tackled this problem by finding the curve that would allow a mass to slide under gravity in the same amount of time, regardless of its starting point, known as the tautochrone problem.
The book is divided into several parts, with the first and fifth sections devoted to the pendulum. In Part I, Huygens describes his work on clocks and attempts to determine longitude at sea. He introduces the concept of tautochronous behaviour of the cycloid curve to correct the erratic motion of pendulums on ships. Part IIA explores the speed and distance travelled by a body falling from rest in successive time intervals, both vertically and horizontally. Part III is an essay on the properties of evolutes of curves, including the cycloid and parabola, and their lengths. Here, Huygens presents his theory of evolutes, building upon the theory of curves. He also addresses the fall of bodies along curves and determines the first value of the force of gravity using a compound pendulum.
Part IV evaluates the centre of oscillation for various shapes in two and three dimensions as candidates for the pendulum bob. The later theorems in this section return to the clock and explore its use in determining a standard of length and the acceleration of gravity. Part V showcases a different type of clock, where the pendulum moves in a circular motion, with the string unwinding from the evolute of a parabola. This section includes 13 theorems related to the theory of centrifugal force in uniform circular motion, which were studied closely but lacked proofs at the time.
Horologium Oscillatorium is notable for being the first modern treatise to idealize a physical problem (the accelerated motion of a falling body) using mathematical parameters and analysing it mathematically. It influenced a generation of physicists and mathematicians, including Newton, Johanne Bernoulli, and Euler. The book received positive reviews in major research journals, with praise for Huygens' invention of the pendulum clock and the elegant mathematics presented.
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Galileo Galilei's law of inertia
Galileo Galilei is credited with first formulating the law of inertia, which states that a body in motion will remain in motion unless it is acted upon by another force. This principle, also known as the first law of motion, was fundamental to Galileo's scientific work, particularly in explaining how the Earth could be spinning and orbiting the Sun without us sensing that motion.
Galileo's law of inertia was deduced from his experiments with balls rolling down inclined planes. He observed that, contrary to Aristotelian mechanics, objects that are not being pushed do not necessarily come to rest. Instead, he found that a body on a smooth, frictionless, horizontal plane will continue to move at a constant speed unless another force stops it. This concept is known as the restricted principle of inertia and enabled Galileo and his followers to establish the science of dynamics, significantly advancing the field of physics.
Galileo's work on the law of inertia was central to his scientific task of explaining the motion of the Earth. He posited that because we are in motion together with the Earth, our natural tendency is to retain that motion, which is why the Earth appears to us to be at rest. This principle of inertia was so important to Galileo because it helped to explain this central scientific conundrum.
The law of inertia was also significant in Galileo's work on astronomy. Furthermore, the law of inertia was important beyond the scope of Galileo's work, influencing later scientists such as René Descartes, who generalized the principle, and Isaac Newton, who formulated his three laws of motion more than eighty years after Galileo's initial investigations. Newton's first law of motion is structurally similar to the law of inertia, stating that a body at rest or moving at a constant speed in a straight line will remain in that state unless acted upon by a force.
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Gauss's Law
The law can be expressed mathematically using vector calculus in integral form and differential form. The integral form of Gauss's law is derived from the definition of electric flux as the integral of the electric field. In this form, the electric field is calculated as the negative gradient of the potential. The differential form of Gauss's law is related to the integral form by the divergence theorem, also known as Gauss's theorem.
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James Clerk Maxwell's kinetic-molecular theory
James Clerk Maxwell, a Scottish physicist and mathematician, made significant contributions to the kinetic-molecular theory, also known as the kinetic theory of gases. This theory originated with Daniel Bernoulli and was further developed by scientists such as John Herapath, John James Waterston, James Joule, and Rudolf Clausius. However, Maxwell played a pivotal role in its advancement, both as an experimenter and a mathematician.
Between 1859 and 1866, Maxwell delved into the kinetic theory of gases and developed the theory of the distributions of velocities in particles of a gas. This work culminated in the creation of a formula known as Maxwell's Distribution, which revolutionised the understanding of temperatures, heat, and molecular movement. The formula, later generalised by Ludwig Boltzmann, became known as the Maxwell-Boltzmann distribution and provided insights into the fraction of gas molecules moving at specific velocities at given temperatures.
In 1867, Maxwell presented a fundamental paper on kinetic gas theory, where he described the evolution of gas in terms of 'moments' of its velocity distribution function. This paper inspired Boltzmann to formulate his renowned kinetic equation, leading to the H-theorem and the exploration of entropy. Maxwell's work laid the foundations for statistical mechanics and enabled a deeper understanding of rarefied gases, which are crucial for studying the upper atmosphere and the fringes of space.
Maxwell's contributions to the kinetic-molecular theory extended beyond his work on gas dynamics. He introduced the concept of velocity distribution or kinetic density, bringing probability into the equation. By computing viscosities and thermal conductivities for gases, he demonstrated that these transport coefficients depended solely on the temperature of the gas rather than its density. This surprising result was later confirmed through experiments conducted by Maxwell himself and published in 1865.
Additionally, Maxwell's work on the kinetic-molecular theory included the first treatment of boundary conditions. He identified a regime where mean free paths were relatively small compared to macroscopic length scales, yet the compressible Navier-Stokes equations were not applicable. His insights into gas dynamics anticipated results obtained by Burnett decades later and demonstrated the explanatory power of kinetic theory in accounting for experimental observations that traditional fluid mechanics could not explain.
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