1. Consider a particle of mass m constrained to move on a frictionless cylinder of radius R, given by the equation ρ=R in cylindrical polar coordinates (ρ, φ, z). Besides the force of constraint, the only force on the mass is force F=-kr directed toward the originUsing z and φ as generalized coordinates find the Lagrangian L, solve Lagrange’s equations and describe the motion. 2. Show that the kinetic energy of any holonomic mechanical system has the form.

T a jk (q) q ( j ) q(k )
j 1 k 1

n

n

. .

3. Consider a double pendulum (fig. 1) made up of two masses, m1 and m2 and two lengths l1 and l2. Find the equation of motion.

Fig. 1

4. A point mass glides without friction on a cycloid, which is given by x= a(v-sinθ) and y=a(1+cosθ) with 0≤v≤2π. Determine the Lagrangian and solve the equation of motion.

5. Two mass points of mass m1 and m2 are connected by a string passing through a hole in a smooth table so that m1 rests on the table surface and m2 hangs suspended. Assuming m2 moves only in a vertical line, what are the generalized coordinates for the system? Write the Lagrange equations for the system and, if possible, discuss the physical significance

any of them might have. Reduce the problem to a single second-order differential equation and obtain a first integral of the equation. What is its physical significance? (Consider the motion only until m1 reaches the hole.). 6. The term generalized mechanics has come to designate a variety of classical mechanics in which the Lagrangian contains time derivatives of qi higher than the first order. Problems

for which

x f x, x, x, t have

been referred to as ‘jerky’ mechanics. Such

equations of motion have interesting applications in chaos theory. By applying the methods of the calculus of variations, show that if there is a Lagrangian of the form

...
Daily Use of Physics
Jason L. McDuffy
University of Memphis
Physics 1 (online)
Project 1
Daily Use of PhysicsPhysics is considered to be a powerful lens that helps people view the everyday world. Physics is reflected in the everyday phenomena, puzzles and toys that offer a variety of interesting challenges leading to deep and interesting problems that derive from science and mathematics. It provides us an understanding of energy, motion and explains these facts as a combination of fundamental particles interacting through fundamental forces. Hence, it is a study of natural phenomena (Oerter, 2006).
Physics is everywhere around us. It is the backbone for any daily life example including electricity, electric light, wristwatch, CD player, cell phone, radio, plasma TV set, computer, refrigerator, and others. Any technology that is used in our daily life is related to this science. In addition, it is believed that physics is a necessity in solving a number of future problems as all forward-looking developments are based on the insights of physics. These potential problems may be related to the development of fuel cells, nuclear fusion as an energy source, and others.
Once upon a time our eyes were the only way for us to see the world. But increasingly sophisticated instruments developed by physicists have allowed...

...Christopher Gooden
Dr. Jan Yarrison-Rice
Physics 101
5 April 2005
Physics in Sports
When many people think of sports, the topic of physics doesn't always come to mind. They usually don't think about connecting athletics with academics. In reality math, science, and especially physics, tie into every aspect of sports. Sports are a commonality that brings nations together, Soccer, known as football to most of the world, is said to an unspoken language, which unties people from different lands through a passion to play a game. Athletics and sports are made by the people who play, watch, and study them. Without all of the enthusiastic participants, there would be no development, education, and intensity that we all know and love about sports. The one component that reigns over the world of sports that most people don't realize is physics, Gravity, uniform circular motion, projectile motion, and constant acceleration are a few that occur in every sport event that has ever taken place.
In the three articles that I chose to write about the concepts of physics are explained in each one. In every article there is the similarity that physics and technology are the reasons for the advances in the sports. In the first article it is evident by the statement, "High-tech bats have so enhanced players' power that some leagues have taken to limiting the number of home runs a team can...

...between the two, grouped in traditional fields such as acoustics, optics, mechanics, thermodynamics, and electromagnetism, as well as in modern extensions including atomic and nuclear physics, cryogenics, solid-state physics, particle physics, and plasma physics.
Physics (from Ancient Greek: φύσις physis "nature") is a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.
Scalars and Vectors
Physics is a mathematical science. The underlying concepts and principles have a mathematical basis. Throughout the course of our study of physics, we will encounter a variety of concepts that have a mathematical basis associated with them. While our emphasis will often be upon the conceptual nature of physics, we will give considerable and persistent attention to its mathematical aspect.
The motion of objects can be described by words. Even a person without a background in physics has a collection of words that can be used to describe moving objects. Words and phrases such as going fast, stopped, slowing down,speeding up, and turning provide a sufficient vocabulary for describing the motion of objects. In physics, we use these words and many...

...Physics End of Year Reflection Paper
At the beginning of this course you were given some overarching enduring understandings and essential questions. These were:
Overarching Enduring Understandings:
Students will uncover and use appropriate scientific models to describe and quantify the nature and interactions of matter and energy.
Students should understand that there is a network of rules and relationships that determine what will happen in a given situation
Students should understand that physics principles are applicable to their everyday lives
Students should find that by studying the rules of nature, the beauty of natural world becomes more alive to them
Overarching Essential Questions:
1. How does physics serve to improve our understanding of physical
systems?
2. How do the principles of physics effect your daily life?
3. Describe something in nature that has become more compelling for you
because of an understanding of physics principles
4. Is it possible to describe the whole natural world (chemical and biological)
with a small number of physical principles? Explain!
5. Is physics a redundant science? Do we now have a clear understanding of
the interactions between matter and energy on all scales? Is technological
application the main thrust of...

...A New Look At Sports
Intro To Cosmology
By: Jarrett Leuta-Douyere
A New Look at Sports
Growing up in a family filled with athletic desire to be great at whatever sport we would participate in and understanding simple physics in Cosmetology, I never realized how much physics comes into play when playing sports. We don’t call it physics when were playing, football, basketball, baseball because it’s just a natural feeling when were throwing a ball or trying to tackle someone. When we began to learn about Newton’s law of Gravity. All sports in the world today have all displayed many aspects of force, motion, gravity, distance and speed but we don’t take the time to realize actually what were doing. Sports have been a big part of my life ever since I was able to stand but I never have once stopped and asked why? Why does a person have tackle with such force and such speed to be able to bring down the runner, or why a baseball can be hit with such force off a bat to be able to hit a home run. Sports are filled with physics that no one understands because we never take the time to ask why, sports are all about physics and the techniques we use to be great at a sport.
When I started to think about all the sports I have played in my life and ask why things happened the way they do I started with the first sport I fell in love with. Baseball was one of the sports that I have...

...Science in the Big City:
Exploring Career Opportunities in the Natural and Physical Sciences
New York City
May 13-18, 2014
Students in the Natural Sciences at the University of Houston-Downtown are generally accomplished and motivated students with strong interests in science. However, students typically have a very limited perception of the science careers available to them outside of medicine. To educate students as to the array of potential careers available in the sciences (not medicine), Drs. J. Johnson and L. Morano are leading an end-of-the semester trip aimed at exposing motivated students in the Natural Sciences to the diverse career opportunities available to them.
This 6-day, 5-night program in New York City will expose students to a unique, behind-the-scenes look at an array of careers and allow students to experience the type of science involved with each career. During the trip students will meet with professional scientists at a variety of research, teaching and government institutions, learn about the nature of these careers, and see firsthand what goes on day-to-day at these diverse career sites. Tentative destinations include the American Museum of Natural History, the New York Botanical Gardens, and various laboratories at New York University. Students will also have the opportunity to tour New York City and take in all the city has to offer.
This trip is not intended for students that are pursuing only professional schools (Medical,...

...Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been the first scientist, and the first Greek philosopher. He was an astronomer, merchant and mathematician, and after visiting Egypt he is said to have originated the science of deductive geometry. He also discovered theorems of elementary geometry and is said to have correctly predicted an eclipse of the sun. Many of his studies were in astronomy but he also observed static electricity. Phythogoras was a Greek philosopher. He discovered simple numerical ratios relating the musical tones of major consonances, to the length of the strings used in sounding them. The Pythagorean theorem was named after him, although this fundamental statements of deductive geometry was most likely first an idea from Egyptian methods of measurements. With the help of his followers he discovered that the earth was a sphere, but he did not believe it revolved around the sun. Democritus was the leader of a group called Atomists. Although they were unable to prove that matter was made up of small particles, they...

...Student Exploration: Fan Cart Physics
Vocabulary: acceleration, force, friction, mass, newton, Newton’s first law, Newton’s second law, Newton’s third law, velocity
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
1. Imagine a horse pulling a cart. What would happen to the speed of the cart if several bags of cement were added to the cart? The speed of the cart would decrease.
2. Suppose several more horses were hitched up to the same cart. How would this affect the speed of the cart? This would affect the speed of the cart because there is more force pulling the positive direction.
Although these questions may seem simple, they form the basis of Newton’s second law of motion. The Fan Cart Physics Gizmo™ can be used to illustrate all three of Newton’s laws.
Gizmo Warm-up
The Fan Cart Physics Gizmo™ shows a common teaching tool called a fan cart. Place fan A on the cart and turn it on by clicking the ON/OFF button below.
1. Look at the blue lines coming from the fan. In which direction is the air pushed? Negative
2. Press Play ([pic]) and observe the cart. In which direction does the cart move? positive direction
By blowing to the left, the fans exert a force on the cart that pushes it to the right. This illustrates Newton’s third law: A force in one direction results in an equal force in the opposite direction.
3. The velocity (v) of the cart is its speed and direction. Click Reset...