Lecture 1 – Introduction 1 Classical Mechanics of Discrete Systems
... The parameters that are used to describe the configuration of a system are called the generalized coordinates. For a complete description of a system, one needs at least as many generalized coordinates as there are degrees of freedom in the system. Depending on how one chooses to describe the system ...
... The parameters that are used to describe the configuration of a system are called the generalized coordinates. For a complete description of a system, one needs at least as many generalized coordinates as there are degrees of freedom in the system. Depending on how one chooses to describe the system ...
Physics 106a – Problem Set 7 – Due Nov 30,... Version 2 November 29, 2004
... two resonant frequencies are almost equal. In this limiting case, if the pendula are set in motion by pulling the upper mass slightly away from the vertical and releasing it, show that subsequent motion is such that at regular intervals one pendulum is at rest while the other has its maximum amplit ...
... two resonant frequencies are almost equal. In this limiting case, if the pendula are set in motion by pulling the upper mass slightly away from the vertical and releasing it, show that subsequent motion is such that at regular intervals one pendulum is at rest while the other has its maximum amplit ...
CH 10
... Total angular momentum is the vector sum of the angular momenta of all the particles in the system L = L1 + L2 + … + LN Total torque is the vector sum of the torques of all the particles in the system = 1 + 2 + … + N ...
... Total angular momentum is the vector sum of the angular momenta of all the particles in the system L = L1 + L2 + … + LN Total torque is the vector sum of the torques of all the particles in the system = 1 + 2 + … + N ...
SCRIBBLE PAD
... • Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. • Force pairs do not act on the same object • The effect of a reaction can be difficult to see • More examples: – Rabbit hopping – Bat hitting ball – Shuttle taking off ...
... • Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. • Force pairs do not act on the same object • The effect of a reaction can be difficult to see • More examples: – Rabbit hopping – Bat hitting ball – Shuttle taking off ...
2. Two-Body Differential Equations-of-Motion
... Consider two masses, m1 and m2 that are spherically symmetric. Although it won’t be proved here, the gravitational field of a spherically symmetric mass is the same as if all the mass were concentrated at a point and may be treated as a particle (as long as the orbit doesn’t fall below the surface o ...
... Consider two masses, m1 and m2 that are spherically symmetric. Although it won’t be proved here, the gravitational field of a spherically symmetric mass is the same as if all the mass were concentrated at a point and may be treated as a particle (as long as the orbit doesn’t fall below the surface o ...
Discussion 1
... difference between the Ui’s is the distance from the mass Mi to the test mass m. For the two righthand masses, r1 = a/2. For the two left-hand masses, r22 = (a/2)2 + a2 = 5a2/4, and so r2 = 5a/2. U = –2 G M m / r1 – 2 G M m / r2 = -4 G M m / a (1 + 1/ 5) (d) If the particle m is released at rest fro ...
... difference between the Ui’s is the distance from the mass Mi to the test mass m. For the two righthand masses, r1 = a/2. For the two left-hand masses, r22 = (a/2)2 + a2 = 5a2/4, and so r2 = 5a/2. U = –2 G M m / r1 – 2 G M m / r2 = -4 G M m / a (1 + 1/ 5) (d) If the particle m is released at rest fro ...
M408N Second Midterm Exam Solutions, October 27, 2011 1) (48
... √ Estimate 628 and 623, each to within .01. (Hint: Use the fact that ...
... √ Estimate 628 and 623, each to within .01. (Hint: Use the fact that ...
Paper Reference(s)
... A uniform ladder, of weight W and length 2a, rests in equilibrium with one end A on a smooth horizontal floor and the other end B on a rough vertical wall. The ladder is in a vertical plane perpendicular to the wall. The coefficient of friction between the wall and the ladder is . The ladder makes ...
... A uniform ladder, of weight W and length 2a, rests in equilibrium with one end A on a smooth horizontal floor and the other end B on a rough vertical wall. The ladder is in a vertical plane perpendicular to the wall. The coefficient of friction between the wall and the ladder is . The ladder makes ...
Powerpoint - University of Pittsburgh
... To describe the thermal motions of small particles, Einstein laid the foundations of the modern theory of stochastic processes and solved the “random walk problem.” Particles spread over time t, distributed on a bell curve. Their mean square displacement is 2Dt. Hence we can read D from the observed ...
... To describe the thermal motions of small particles, Einstein laid the foundations of the modern theory of stochastic processes and solved the “random walk problem.” Particles spread over time t, distributed on a bell curve. Their mean square displacement is 2Dt. Hence we can read D from the observed ...
Study Guide - Motion Name Key Date Pd 1. An object is in ___
... 28. Explain the difference between balanced and unbalanced forces. Balanced forces acting on an object equal zero, unbalanced forces are when all the forces acting on an object do not equal zero. 29. Suppose you were on in-line skates and you toss a backpack full of heavy books toward your friend. W ...
... 28. Explain the difference between balanced and unbalanced forces. Balanced forces acting on an object equal zero, unbalanced forces are when all the forces acting on an object do not equal zero. 29. Suppose you were on in-line skates and you toss a backpack full of heavy books toward your friend. W ...
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.