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Euler's Disk
Euler's Disk, invented between 1987 and 1990 by Joseph Bendik, is a trademark for a scientific educational toy. It is used to illustrate and study the dynamic system of a spinning and rolling disk on a flat or curved surface. It has been the subject of several scientific papers. Discovery Joseph Bendik first noted the interesting motion of the spinning disk while working at Hughes Aircraft (Carlsbad Research Center) after spinning a heavy polishing chuck on his desk at lunch one day. The apparatus is a dramatic visualization of energy exchanges in three different, tightly coupled processes. As the disk gradually decreases its azimuthal rotation, there is also a decrease in amplitude and increase in the frequency of the disk's axial precession. The evolution of the disk's axial precession is easily visualized in a slow motion video by looking at the side of the disk following a single point marked on the disk. The evolution of the rotation of the disk is easily visualized in sl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Disk
Euler's Disk, invented between 1987 and 1990 by Joseph Bendik, is a trademark for a scientific educational toy. It is used to illustrate and study the dynamic system of a spinning and rolling disk on a flat or curved surface. It has been the subject of several scientific papers. Discovery Joseph Bendik first noted the interesting motion of the spinning disk while working at Hughes Aircraft (Carlsbad Research Center) after spinning a heavy polishing chuck on his desk at lunch one day. The apparatus is a dramatic visualization of energy exchanges in three different, tightly coupled processes. As the disk gradually decreases its azimuthal rotation, there is also a decrease in amplitude and increase in the frequency of the disk's axial precession. The evolution of the disk's axial precession is easily visualized in a slow motion video by looking at the side of the disk following a single point marked on the disk. The evolution of the rotation of the disk is easily visualized in sl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often discuss ideal test results that would occur in a ''perfect'' vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is considerably lower than atmospheric pressure. The Latin term ''in vacuo'' is used to describe an object that is surrounded by a vacuum. The ''quality'' of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%. But hig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that category was abolished in 1995). The radian is defined in the SI as being a dimensionless unit, with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing. Definition One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, \theta = \frac, where is the subtended angle in radians, is arc length, and is radius. A right angle is exactly \frac radians. The rotation angle (360°) corresponding to one complete revolution is the length of the circumference divided by the radius, which i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
G-force
The gravitational force equivalent, or, more commonly, g-force, is a measurement of the type of force per unit mass – typically acceleration – that causes a perception of weight, with a g-force of 1 g (not gram in mass measurement) equal to the conventional value of gravitational acceleration on Earth, ''g'', of about . Since g-forces indirectly produce weight, any g-force can be described as a "weight per unit mass" (see the synonym specific weight). When the g-force is produced by the surface of one object being pushed by the surface of another object, the reaction force to this push produces an equal and opposite weight for every unit of each object's mass. The types of forces involved are transmitted through objects by interior mechanical stresses. Gravitational acceleration (except certain electromagnetic force influences) is the cause of an object's acceleration in relation to free fall. The g-force experienced by an object is due to the vector sum of all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Singularity
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the real function : f(x) = \frac has a singularity at x = 0, where the numerical value of the function approaches \pm\infty so the function is not defined. The absolute value function g(x) = , x, also has a singularity at x = 0, since it is not differentiable there. The algebraic curve defined by \left\ in the (x, y) coordinate system has a singularity (called a cusp) at (0, 0). For singularities in algebraic geometry, see singular point of an algebraic variety. For singularities in differential geometry, see singularity theory. Real analysis In real analysis, singularities are either discontinuities, or discontinuities of the derivative (sometimes also discontinuities of higher order derivatives). There are four kinds of discon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ..., an integral assigns numbers to functions in a way that describes Displacement (geometry), displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with Derivative, differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keith Moffatt
Henry Keith Moffatt, FRS FRSE (born 12 April 1935) is a Scottish mathematician with research interests in the field of fluid dynamics, particularly magnetohydrodynamics and the theory of turbulence. He was Professor of Mathematical Physics at the University of Cambridge from 1980 to 2002. Early life and education Moffatt was born on 12 April 1935 to Emmeline Marchant and Frederick Henry Moffatt''.'' He was schooled at George Watson's College, Edinburgh, going on to study Mathematical Sciences at the University of Edinburgh, graduating in 1957. He then went to Trinity College, Cambridge, where he studied mathematics and, 1959, he was a Wrangler. In 1960, he was awarded a Smith's Prize while preparing his PhD. He received his PhD in 1962, the title of his dissertation was ''Magnetohydrodynamic Turbulence.'' Career After completing his PhD, Moffatt joined the staff of the Mathematics Faculty in Cambridge as an Assistant Lecturer and became a Fellow of Trinity College. He was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nature (journal)
''Nature'' is a British weekly scientific journal founded and based in London, England. As a multidisciplinary publication, ''Nature'' features peer-reviewed research from a variety of academic disciplines, mainly in science and technology. It has core editorial offices across the United States, continental Europe, and Asia under the international scientific publishing company Springer Nature. ''Nature'' was one of the world's most cited scientific journals by the Science Edition of the 2019 ''Journal Citation Reports'' (with an ascribed impact factor of 42.778), making it one of the world's most-read and most prestigious academic journals. , it claimed an online readership of about three million unique readers per month. Founded in autumn 1869, ''Nature'' was first circulated by Norman Lockyer and Alexander Macmillan as a public forum for scientific innovations. The mid-20th century facilitated an editorial expansion for the journal; ''Nature'' redoubled its efforts in exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heads Or Tails
Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking obverse and reverse, which side is showing when it lands, in order to choose between two alternatives, heads or tails, sometimes used to resolve a dispute between two parties. It is a form of sortition which inherently has two possible outcomes. The party who calls the side that is facing up when the coin lands wins. History Coin flipping was known to the Romans as ''navia aut caput'' ("ship or head"), as some coins had a ship on one side and the head of the Roman Emperor, emperor on the other. In England, this was referred to as ''cross and pile''. Process During a coin toss, the coin is thrown into the air such that it rotates edge-over-edge several times. Either beforehand or when the coin is in the air, an interested party declares "heads" or "tails", indicating which side of the coin that party is choosing. The other party is assigned the opposite side. Depending on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
US Quarter
The quarter, short for quarter dollar, is a United States coin worth 25 cents, one-quarter of a dollar. The coin sports the profile of George Washington on its obverse, and after 1998 its reverse design has changed frequently. It has been produced on and off since 1796 and consistently since 1831. It has a diameter of 0.955 inch (24.26 mm) and a thickness of 0.069 inch (1.75 mm). Its current version is composed of two layers of cupronickel (75% copper, 25% nickel) clad on a core of pure copper. With the cupronickel layers comprising 1/3 of total weight, the coin's overall composition is therefore 8.33% nickel, 91.67% copper. Its weight is 5.670 grams (0.1823 troy oz, or 0.2000 avoirdupois oz). Designs before 1932 The choice of a quarter-dollar as a denomination, as opposed to the or the 20-cent piece that is more common elsewhere; it originated with the practice of dividing Spanish milled dollars into eight wedge-shaped segments, which gave rise to the n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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