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Wednesday, February 13, 2008
Wednesday, February 13, 2008

... Newton’s First Law and Inertial Frames Aristotle (384-322BC): A natural state of a body is rest. Thus force is required to move an object. To move faster, ones needs larger forces. Galileo’s statement on natural states of matter: Any velocity once imparted to a moving body will be rigidly maintaine ...
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... object to find the motion of that particular object. The ”physics” of the interactions between particles is described by the force that one particle exerts on another, which can usually be expressed in a simple way. As objects move, the forces change in time, and the resulting motion can be complica ...
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... as it enters the block of wood, which prevents it from passing all the way through it. Most of the momentum transfers and a max KE is lost. •  The third bullet bounces off the block transferring “all of its own momentum” and then borrowing some more from the block. This has the most momentum transfe ...
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... More on Conservation of Linear Momentum in a Two Body System From the previous lecture we’ve learned that the total momentum of the system is conserved if no external forces are exerted on the system. ...
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Brownian motion



Brownian motion or pedesis (from Greek: πήδησις /pˈɪːdiːsis/ ""leaping"") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the quick atoms or molecules in the gas or liquid. Wiener Process refers to the mathematical model used to describe such Brownian Motion, which is often called a particle theoryThis transport phenomenon is named after the botanist Robert Brown. In 1827, while looking through a microscope at particles trapped in cavities inside pollen grains in water, he noted that the particles moved through the water but was not able to determine the mechanisms that caused this motion. Atoms and molecules had long been theorized as the constituents of matter, and many decades later, Albert Einstein published a paper in 1905 that explained in precise detail how the motion that Brown had observed was a result of the pollen being moved by individual water molecules. This explanation of Brownian motion served as definitive confirmation that atoms and molecules actually exist, and was further verified experimentally by Jean Perrin in 1908. Perrin was awarded the Nobel Prize in Physics in 1926 ""for his work on the discontinuous structure of matter"" (Einstein had received the award five years earlier ""for his services to theoretical physics"" with specific citation of different research). The direction of the force of atomic bombardment is constantly changing, and at different times the particle is hit more on one side than another, leading to the seemingly random nature of the motion.The mathematical model of Brownian motion has numerous real-world applications. For instance, Stock market fluctuations are often cited, although Benoit Mandelbrot rejected its applicability to stock price movements in part because these are discontinuous.Brownian motion is among the simplest of the continuous-time stochastic (or probabilistic) processes, and it is a limit of both simpler and more complicated stochastic processes (see random walk and Donsker's theorem). This universality is closely related to the universality of the normal distribution. In both cases, it is often mathematical convenience, rather than the accuracy of the models, that motivates their use.
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