Other Physics Commons^™

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 …

Second Law And Entropy

Calculus-Based General Physics

Suppose you get into your car and drive to _________.* During this trip, (1) the burning of the gasoline in the engine cylinders converts chemical energy into thermal energy of the gases -- that is, they become very hot; (2) the expansion of these hot gases turns the crankshaft, performing work; and (3) this work, transmitted to the wheels, gives the car kinetic energy -- which must be continually replenished, because of depletion by friction and air resistance. At the end of this trip, ____ gallons of gasoline have been converted into water vapor, carbon dioxide, and sundry less desirable …

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.

Ohm's Law

Calculus-Based General Physics

Recently you have heard many ways of reducing energy consumption in the home. One of the suggested ways is to use 60-W liqht bulbs rather than 100-W bulbs; another is to cut back on the use of electrical appliances. You readily identify these suggestions with decreasing the amount of "electricity" beinq transported through the wires coming into your home.

You were warned quite early in life not to stick a metal knife into the toaster to force out burning bread; you either unplug the toaster or use a utensil with a wooden handle. Why? Because you were warned of the …

Rotational Dynamics

Calculus-Based General Physics

A diver, in making several turns in the air, grabs his knees to achieve a high rate of rotation, and a skater does much the same thing when she goes into a spin with arms and legs extended but brings them in close to her body for the extremely rapid part of this motion. This module considers the physics describing these motions, and those of other rotational systems -- starting or stopping a record turntable (or a washing-machine tub), unwinding of winch cord as a bucket is dropped into a well, etc.

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 …

Conservation Of Energy

Calculus-Based General Physics

Imagine a bicycle rider coasting without pedaling along a road that is very smooth but has a lot of small hills. As he coasts up a hill, the force of gravity will, of course, slow him down; but it speeds him up again as he goes down the other side. We say that gravity is a conservative force because it gives back as much kinetic energy (KE) to the cyclist when he returns to a lower level, as it took away when he ascended to the top. We therefore assign a gravitational potential energy (PE) U_g to the cyclist, …

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 …

01 Content And Prerequisite Description: Module Sequence/Roadmap With Links

Calculus-Based General Physics

What is the proper order to address the topics in the STUDY MODULES FOR CALCULUS-BASED GENERAL PHYSICS ? Do you need to master "A" before moving on to "B"?

These are prerequisite charts and suggested sequences for study modules of the Calculus-Based Physics Personalized System of Instruction:

I. Mechanics, Sound, Heat

II. Electricity, Magnetism, Light

Each "road map" is linked to the texts of the modules in this repository.

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 …

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 …

Capacitors

Calculus-Based General Physics

Capacitors are important components of electronic circuits and of electrical machinery and power grids. You can find large oil-insulated capacitors on powerline poles or small ceramic-insulated capacitors in a radio. In each application the capacitor is used to store electrical charge and electrical energy - for example, sometimes for a short time in an alternating-current cycle, sometimes for a long time until the energy is needed, as in a strobe light for a camera. Your body can be a capacitor, storing up enough charge and energy to cause a painful spark when the capacitor discharqes.

Practical capacitors are basically two …

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 …

Reflection And Refraction

Calculus-Based General Physics

Sight is certainly one of our most important senses and depends on the interaction of electromagnetic waves in the visible portion of the spectrum with the eye. The use of materials that reflect light and that refract or "bend" light extends throughout our industrialized society. In this module we deal with light traveling in two dimensions and encounterinq the boundaries between media under those conditions in which the wavelength is small compared with the size of the obstacles or apertures. Under such conditions, since diffraction and interference effects are negligible, the principal phenomena occurring at the interfaces, reflection and refraction, …

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" …

Wave Properties Of Light

Calculus-Based General Physics

How do Polaroid sunglasses reduce glare? What evidence is there for an expanding universe? You will learn the answer to these two questions by considering some properties of light. Gamma rays, x rays, light (ultraviolet, visible, and infrared) and radio waves are all forms of electromagnetic radiation and therefore share the same basic properties as mentioned in this module and the module Maxwell's Predictions. The basic difference among these types of electromaonetic radiation is their wavelengths or frequencies.