INTRODUCTION
We know the importance of Angular Momentum in Classical Mechanics; the total angular momentum of an isolated physical system is a constant of the motion. For example, if a point particle P, of mass m, is moving in a central potential (one which depends only on the distance between P and a fixed point O), the force to which P is subjected is always directed towards O. Its moment with respect to O is consequently zero, and the angular momentum theorem implies that derivative of L (Angular momentum of P with respect to O) with respect to time is zero.
This fact has important consequences: the motion of the particle P is limited to a fixed plane (the plane passing through O and perpendicular to the angular momentum L); moreover, this motion obeys the law of constant areal velocity (Kepler’s Second Law).
All these properties have their equivalents in Quantum Mechanics. With the angular momentum L of a classical system is associated with an observable L, actually a set of three observables, Lx, Ly, and Lz, which correspond to the three components of L in a Cartesian Frame. These three observables commute with the Hamiltonian H for a particle in the central potential V(r). This property simplifies the determination and classification of eigenstates of H.
Quantization of Angular Momentum: the component, along a fixed axis, of the intrinsic angular momenta are quantized, which enables us to understand atomic magnetism, the Zeeman Effect, etc. We shall denote by
Eventually Galileo Galilei (1564 – 1642) came to popularity, rejecting the Aristotelian notions of motion (O'Connor, J.J., & Robertson, E. F., 2002). He showed that speed does not increase continuously and that impetus does not exist, and argued that once motion starts it would remain forever, if not imparted. This idea is very similar to Isaac Newton’s later ideas of inertia and his
that by making one simple assumption, that all objects in the universe attract one another
According to Merriam-Webster’s a hero is defined as “exhibiting or marked by courage and daring” or a person who’s “supremely noble or self-sacrificing”, meaning you don’t have to be a superhero to be considered heroic. Doing something that has a significant effect on society or changing the way something appears to be, makes one heroic; therefore, Albert Einstein is heroic in numerous ways.
Heisenberg realized that the uncertainty relations had profound implications. Heisenberg set himself to the task of finding the new quantum mechanics to explain what his theories observed. He relied on what can be observed, namely the light emitted and absorbed by the atoms. By July 1925, Heisenberg wrote his answer in a paper. The basic idea of Heisenberg's paper was to get rid of the orbits in atoms and to arrive at new mechanical equations. Heisenberg’s approached focused mainly on the particle nature of electrons. The mathematics Heisenberg used were tables commonly used for multiplication of arrays of numbers-mathematical objects known as matrices. Using the mathematics of matrices, scientists had at last a new mechanics for calculating the quantum behavior of particles. Heisenberg, and others showed that the new quantum mechanics could account for many of the properties of atoms and atomic events.
This will lead to an explanation of motion, the development of the calculus, and the establishment of basic laws of modern physics.
The Law of ellipses, which means that each planet travels around the sun in an ellipses.
-When the size of the system is very large compared to the de Brogue wavelength, the Newton’s laws of motion and quantum mechanics overlap.
Galileo was the first European to make systematic observations of the heavens through his improved invention of the telescope. Through his telescope, Galileo made a series of discoveries. Galileo’s observations demolished among the traditional cosmology of what the universe seemed to be composed of. Not only did Galileo make astonishing discoveries, but he was also offered a new position from Grand Duke Cain II of Florence, as his court mathematician. During this time, Galileo was told that he could continue to discuss Copernicanism, as long as he would maintain everything as mathematical supposition, and not as facts. Due to the Inquisitions response, the church attacked the Copernican system since it threaten the Scripture and its’ entire conception of the universe. The new system rose'd much uncertainty that seemed as prudent to simply condemn it. In 1633, Galileo was found guilty of teaching the condemned Copernican system and was then forced to be placed under house arrest. He spent the remaining eight years of life studying mechanics. The principal of motion was the one of the problems that fell under the heading of mechanics. At the end, Galileo made two contributions to the problem of motion. He demonstrated by experimenting uniform force to accelerate
In today's world, we have very advanced technology. There have been many new technological and medical advancements as we entered the new century. The Internet allows us to shop, talk, and find valuable information on very scarce topics, and even check stocks with a simple click of a button. Medical advancements had recently been discovered on "The Human Genome Projects," the first gene was mapped and within a short period of time we will have mapped out all the genes in a human chromosome. This is absolutely amazing because we will now be able to reveal the many causes of serious deadly diseases. Throughout the years, we have gained the technology to send astronauts into space to gather new information about our
The discovery of these laws, laid down a basic foundation for the physics of motion. Newton's three laws of gravity changed the way in which the world was perceived, because of their accuracy in describing many unexplained phenomenons.3 They explained what happens as a result of different variables, but most importantly, they explained why and how these actions happen. Like many of Isaac Newtons ideas and theories, the three laws of motion had a profound impact on the scientific community. The three laws of motions provided an explanation for almost everything in macro physics. Macro Physics is the branch of physics that deals with physical objects large enough to be observed and treated directly.4 This allowed for many new advancements in physics because the foundation had been build for others to develop upon. Isaac Newton published these findings in his revolutionary book “The Principa”. The Principa was revolutionary book because it organized the bulk of his life’s work, More importantly the
In Metaphysics XII, Aristotle elaborates on a need for a “first mover that initiates motion without being moved” (Met. 12.7, 1072a26). This primary, or unmoved mover, he believes is the source of all motion in the universe. In this essay, I will explain his conception of such a mover. I will then elaborate on how this unmoved mover initiates motion. Finally, I will explain his rationale for believing there is such a mover.
Angular momentum is the momentum an object has as it rotates around an axis. Angular momentum is determined by the mass and velocity the object has. Rotational inertia is the body’s resistance to rotate, in this case it refers to the body’s resistance to turn and complete the summersault. Rotational inertia
His first law states, “The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.” As shown in Figure 1, The Sun is not at the focus of the ellipse, but is instead at one focus [usually there is nothing at the other focus of the ellipse]. The planet then trails the ellipse in its orbit, which implies that the Earth-Sun distance is continually changing as the planet goes around its orbit. Kepler’s second law states, “The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.” As shown in Figure 2, an imaginary line from the center of the sun to the center of a planet sweeps out the same area in a given time. This means that planets move faster when they are closer to the sun. Kepler’s third and final law states, “The time taken by a planet to make one complete trip around the sun is its period. The ratio of the squares of periodic times for two planets is equal to the ratio of the cubes of their mean distances from the sun.” Kepler’s third law indicates that the time taken by a planet to orbit the Sun increases quickly with the radius of its orbit ("Johannes Kepler: The” 1-4). Kepler’s laws challenged Aristotelean and Ptolemaic astronomy. His statement that the Earth
“I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.” – Sir Isaac Newton (Brewster, Memoirs of Newton, 1855)
Though these are not the only important elements of orbital mechanics, there is also the period (P) and true anomaly (v) which is “the angular distance of a point in an orbit past the point of periapsis.