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Rotational Motion

Calculus-Based General Physics

There is a motion of a system of masses that is as simple as the motion of a point mass on a straight line. It is the rotation of a rigid body about a fixed axis. For example, we live on a rotating earth, use rotating devices such as a potter's wheel or a phonograph turntable, and test our luck with a spinning roulette wheel. All of these are objects whose motion is described by the time dependence of a single variable, the angle of rotation. We shall study the angular equivalent of uniformly accelerated motion for some rotating objects. …

Applications Of Newton's Laws

Calculus-Based General Physics

Perhaps at some time you have had occasion to swing a massive object at the end of a rope. Maybe you have watched a parent swing a child around by his outstretched arms or have been fortunate enough to watch an athlete throw the hammer. But all of you have heard or watched an automatic washer go through a spin-dry cycle. How was this spinning drum with holes in its periphery able to speed up the "drying" process? The clothes were too large to pass through the holes in the drum and were "held" in a circular path but the …

Simple Harmonic Motion

Calculus-Based General Physics

Have you ever felt you were the slave of a clock? Clocks are mechanisims that include a pendulum or balance wheel whose repeated patterns of movement define equal time intervals, one after another. Such repeated movements are called periodic motion. Periodic motion may occur when a particle or body is confined to a limited region of space by the forces acting on it and does not have sufficient energy to escape.

In this module you will study the special kind of periodic motion that results when the net force acting on a particle, often called the restoring force, is directly …

Faraday's Law

Calculus-Based General Physics

Consider the electric light you may be using to read this module by and the influence on your life style of the vast amounts of electrical energy produced in the United States. This module treats the fundamental principle that allows for the transformation of mechanical energy into electrical energy. The physical law that governs the production of electric current is named after its discoverer, Michael Faraday.

Traveling Waves

Calculus-Based General Physics

"For many people -- perhaps for most -- the word "wave" conjures up a picture of an ocean, with the rollers sweeping onto the beach from the open sea. If you have stood and watched this phenomenon, you may have felt that for all its grandeur it contains an element of anticlimax. You see the crests racing in, you get a sense of the massive assault by the water on the land -- and indeed the waves can do great damage, which means that they are carriers of energy -- but yet when it is all over, when the wave …

Temperature, Heat, And Thermodynamics: First Law

Calculus-Based General Physics

How can we keep track of energy as it is transferred from one system to another? How can we calculate the amount of internal energy -- a quantity that seems to be hidden within the very "guts" of matter? Further, what is the difference between temperature and heat, and between heat and work?

This module focuses on the first of two central thermodynamic principles: the conservation of energy, or, as it is sometimes called, the first law of thermodynamics. The second basic principle, which deals with the inevitable increase of a quantity called entropy, is the subject of another module …

Alternating-Current Circuits

Calculus-Based General Physics

The electric clock on the wall, radio and television, the incredibly rapid handling
of information by computers, and the transmission of signals by our own nerves
are among countless devices and effects that depend on circuits in which currents
or voltages vary with time. Alternatinq-current (ac) circuits, in which charges
oscillate back and forth in a wire in such a way that the average current is
zero,are among the simpler time-varying circuits. In this module you will study
the behavior of simple ac circuits containing resistors, inductors, and capacitors.

0 Introduction To Study Modules For Calculus-Based General Physics

Calculus-Based General Physics

These modules were prepared by fifteen college physics professors for use in self-paced, mastery-oriented, student-tutored. calculus-based general physics courses. This style of teaching offers student's a personalized system of instruction (PSI), in which they increase their knowledge of physics and experience a positive learning environment. We hope our efforts in preparing these modules will enable you to try and enjoy teaching physics using PSI.

This is the second printing of the CBP modules. We have tried to remove all of the errors from this material. No doubt, we missed a few, please write to us and tell us any that …

Gravitation

Calculus-Based General Physics

The members of the solar system -- the Sun, the Moon, and the planets -- have held a strong fascination for mankind since prehistoric times. The motions of these heavenly bodies were thought to have important specific influences on persons' lives -- a belief that is reflected even today in horoscopes and astrological publications. A revolution in man's thinking that occurred about four hundred years ago established the concept of a solar system with planets orbiting about the Sun and moons orbiting about some of the planets. Copernicus, Kepler, Galileo, and Newton were the four scientific leaders chiefly responsible for …

Impulse And Momentum

Calculus-Based General Physics

You have already learned that you stub your toe harder trying to kick larger masses. Now imagine another unpleasant activity: catching a bowling ball. This gets harder to do as the ball is dropped from higher places. The difficulty depends both on the ball's mass and its velocity just before you apply the stopping force. This force can be applied in different ways. Any winner of an egg-throwing contest will tell you the way to stop an object with the least force is to spread the stopping process out over a maximum time.

This module will develop the above "folk …

Newton's Laws

Calculus-Based General Physics

When a body is at rest, we know from experience that it will remain at rest unless something is done to change that state. A heavy box on the floor will stay in place unless it is pushed or pulled. We walk without fear beside a massive rock on level ground because we know it won't suddenly move and crush us.

Undoubtedly you have leaned against a chair only to have it move and send you scurrying for your balance. Did you then question the relationship of the interaction between you and the chair to the ensuing motion of the …

Trigonometry

Calculus-Based General Physics

Many of the applications of physics will require you to have a thorough knowledge of the basic properties of right triangles, i.e., triangles that have one angle equal to 90°.

The trigonometric functions are defined with respect to a right triangle as follows:

sin θ = y/r

cos θ = x/r

tan θ = y/x

The values of the trigonometric sine, cosine, and tangent functions for a given θ can be determined from a table such as in the appendix to your text or the last page of this module. You can also get the values by use of most …

Work And Energy

Calculus-Based General Physics

Energy is much in the news lately. The term "energy" usually refers to the inherent ability of a material system, such as a person, a flashlight battery, or rocket fuel, to bring about changes in its environment or in itself. Some common sources of energy are the fuel used to heat hot water, the gasoline that propels a car, the dammed water that drives the turbine in a hydroelectric plant, and the spinning yo-yo that can climb up its own string. Inanimate energy sources are of central importance in raising the standard of living of mankind above the subsistence level. …

Sound

Calculus-Based General Physics

We, much more than our ancestors, are constantly being bombarded by sound. We hear, and are more or less aware of, music, air hammers, television sets, jet planes, conversation, engines, sirens, etc., throughout the day. A sophisticated audio industry tries to improve the quality of musical sound. At the other end of the quality scale, noise pollution is a serious concern, which probably affects our lives more than we realize.

In order to deal with sound, we should have some idea of what it is. What factors determine whether a sound is pleasing or grating? How is sound transmitted? How …

Diffraction

Calculus-Based General Physics

Have you ever wondered why you can hear around corners, but cannot see around them? You know that light and sound are waves, and should therefore share the same basic properties. Why then do they seem so different in the property of their "shadows"?

In this module you will learn that light does exhibit all the bending properties of sound and water waves. The effect, however, depends on the size of the obstacle compared to the wavelength. It is only the largeness of everyday obstacles compared to the very small wavelength of light that deemphasizes the bending, or diffraction, of …

Auroral Energy Input From Energetic Electrons And Joule Heating At Chatanika, Vincent B. Wickwar, M J. Baron, R D. Sears

All Physics Faculty Publications

With the incoherent scatter radar at Chatanika, Alaska, a wide variety of measurements can be made related to the ionosphere, magnetosphere, and neutral atmosphere. A significant parameter is the amount of energy transferred from the magnetosphere into the ionosphere and neutral atmosphere during periods of auroral activity. In this report we examine a procedure whereby the incident energy flux of auroral electrons is ascertained from radar measurements. As part of the process we compare radar-determined fluxes with those ascertained from simultaneous photometric observations at 4278 Å. The fluxes obtained by both techniques had similar magnitudes and time variations. If we …

Double Reflection Dips From Grating Ruled Semiconductors, L. F. Teng, Ralph William Alexander, Robert John Bell, B. Fischer

Physics Faculty Research & Creative Works

The Double Reflectivity Dips, Previously Observed by Fischer Et Al. and Anderson Et Al., Which Appeared in the Reflection Spectra of Grating Surfaces On, the Te‐doped Semiconductors GaAs and InSb Around Both the Plasmon and Phonon Frequencies Have Been Measured in More Detail. in the Plasmon Region, Several Possible Explanations of the Phenomenon Are Discussed, But the Favored Explanation Involves Surface Damage. a Simple Two‐region Reflectivity Equation Checked with a Rigorous Grating Theory is Proposed and is Shown to Fit the Data Well. Copyright © 1975 WILEY‐VCH Verlag GmbH & Co. KGaA

Photoionization Of The 6p32,122 Fine-Structure Levels In Cesium, Kaare J. Nygaard, Robert E. Hebner, James A. Jones, Robert J. Corbin

Physics Faculty Research & Creative Works

The relative photoionization cross sections for cesium atoms selectively excited to the 6P32,122 states have been measured in a triple-crossed-beam experiment. A cesium discharge lamp produced resonant wavelengths of 8521 and 8944 for the excitation process. A Hg-Xe lamp combined with a grating monochromator was used for the actual ionization in the wavelength region from 2500 to 5000. Background counts due to photoionization of ground-state cesium atoms and dimers as well as various surface effects were discriminated against by chopping the excitation light source. The data are compared with results from radiative-recombination measurements in which the fine-structure levels are not …

Personalized System Of Instruction (Psi): An Alternative, James G. Buterbaugh, Robert Fuller

Personalized System of Instruction (PSI), or Keller Plan, Materials

Buterbaugh and Fuller discuss the Personalized System of Instruction--what it is, how it can (or cannot) be evaluated, and some problems which may be encountered with its use. If the lecture-taught course has instructors meeting the students as adversaries, continually answering redundant questions, haggling over half-credit for half-correct answers, and generally finding most students being inhibited by the lock-step timing of a lecture course, then PSI is an alternative. Extensive acceptance and employment of this alternative mode of instruction should cause instructional developers to take another look at the essential features of the system. PSI has been widely employed by …

Ampère's Law

Calculus-Based General Physics

Everyone has seen a bar magnet in the form of a compass or a door catch. Anyone who has ever casually played with magnets or magnetic toys knows that magnets interact with other magnets; i.e., a magnet experiences a force caused by thp presence of an external magnetic field produced by the other magnet. A wire carrying a current experiences a force caused by the presence of a nearby magnet (as you saw in the module Magnetic Forces). We then expect the converse to also hold true, i.e., that the bar magnet will also experience a force from the presence …

Equilibrium Of Rigid Bodies

Calculus-Based General Physics

Most of the objects that one sees are in a state of equilibrium, that is, at rest or in a state of uniform motion. Many man-made structures are designed to achieve and sustain a state of equilibrium, and this, in turn, sets requirements to the materials (their sizes and shapes) that can be used. This module will give you some practice in analyzing the forces that result in equilibrium. From this analysis, if you are given the values of an appropriate set of forces you can find the remaining ones. On the other hand, in designing a stable system you …

Inductance

Calculus-Based General Physics

Anyone who has ever grabbed an automobile spark-pluq wire at the wrong place, with the engine running, has an appreciation of the ability of a changinq current in (part of) a coil of wire to induce an emf in the coil. What happens is that the breaker contacts open, suddenly interrupting the current, and causing a sudden large change in the magnetic field through the coil; according to Faraday's law, this results in a (large) induced emf. In general, the production of an emf in a coil by a changing magnetic field due to a current in that same coil …

Introduction To Quantum Physics

Calculus-Based General Physics

You have probably encountered a system known as an "electric eye," which senses light from an artificial source or the sun. This information is used to open doors, count pedestrian or auto traffic, turn on lights at sunset, read holes in punched card, and for a host of other applications. Most of these devices are based on the photoelectric effect, which is the light-induced emission of electrons from atoms.

The photoelectric effect completely baffled physicists at the time of its discovery. Einstein's explanation of this process, which won the Nobel Prize in 1921, was a major part of the twentieth-century …

Maxwell's Predictions

Calculus-Based General Physics

With this module, you will reach a milestone in your study of electromagnetic phenomena. From past modules, you now have (at your fingertips, hopefully!) the same basic laws of electromagnetism that Maxwell collected together in the nineteenth century. However, as powerful as these laws were, Maxwell found that there was a basic flaw -- a logical inconsistency -- in the one known as Ampere's law. He was able to deduce (in advance of any direct experimental test) precisely the correction that was needed. With this correction, the addition of what is called the "displacement-current" term to Ampere's law, it follows …

Calculus

Calculus-Based General Physics

Differentiation of a function, say f(x), is a mathematical operation which yields a second function called the derivative of f [symbolized by f '(x) or dy/dx]. This procedure is represented in the diagram, which shows

Input                  Differentiation Operation               Output

f(x)                                   →                               f ' (x) = df/dx

the function f(x) being input to an "analytical machine" that manufactures as output the derivative of f. A detailed mathematical prescription for the differentiation operation is nontrivial. It usually involves a quarter or semester course, which requires time, attention, and effort on the student's part.

Partial Derivatives

Calculus-Based General Physics

If we have a function of more than one independent variable, then we can define a partial derivative with respect to one of the variables, which is simply the derivative of the function with all the other variables fixed, The notation using ∂, which we will use below, tells you it is a partial derivative, For example, suppose we have the function y that depends on the independent variables x and t:

y = A sin(kx – ωt),

where A, k, and ω are constants, Then, "the partial derivative of y with respect to x" …

Can Psi Help Him?

Personalized System of Instruction (PSI), or Keller Plan, Materials

PSI (Personalized System of Instruction) can help students learn!

If the lecture-taught course has you meeting the students as adversaries, continually answering redundant questions, haggling over half credit for half correct answers, and generally finding your students being inhibited by the lock-step timing of a lecture course, then PSI is an alternative.

It is also the title of a film, PSI: An Alternative, that imaginatively and graphically outlines an intriguing and dynamic system for learning.

PSI (also known as the Keller Plan) is self-paced, mastery oriented, student tutored for junior college and college level instruction with classes of all sizes …

Inclusion Of Rectangular And Triangular Geometries In The Space-Dependent Kinetics Code, Fx2, Ted Perry

Undergraduate Honors Capstone Projects

The computer code FX2 is used to model liquid-metal fast-breeder reactors now being developed by the U. S. Atomic Energy Commission. These reactors differ from thermal reactors in that they have no moderator material in their cores and thus operate at mean neutron energies of 100 keV or more as opposed to neutron energies of less than 1 keV for thermal reactors. Also these reactors have the advantage that as a consequence of the high neutron energies, these reactors can be used to "breed" their own fuel: enriched ²³⁸U placed in the core is changed into plutonium which can …

Supersaturated Zincate Solutions, W. Van Doorne, T. P. Dirkse

University Faculty Publications and Creative Works

A study of supersaturated zincate solutions is made using light scattering and nuclear magnetic resonance techniques. The results indicate strongly that the excess zinc is present as a solute species rather than in a colloidal form. The solute species appears to be the same as that in solutions of ZnO in aqueous KOH, viz., Zn(OH)42-. There is no strong evidence to indicate the presence of other solute species.

Strain Effects On The Esr Spectrum From Antimony Donors In Germanium, Edward Boyd Hale, John R. Dennis, Shih Hua Pan

Physics Faculty Research & Creative Works

The electron-spin-resonance spectra from surface-strained (but not externally stressed) antimony-doped germanium are investigated in detail. Experimental data are given for the linewidth, line asymmetry, and line-shape reversal feature as well as for the changes in donor concentration, temperature, and surface conditions. The donors of interest occur in a surface layer several microns thick. A theoretical analysis is based on the Kohn-Luttinger formulation for a shallow donor electron, which is forced by surface strain to predominately occupy a [111] conduction-band valley minimum. A substantial distribution in strain among the donor sites is necessary to account for the line-structure features. These features …