1. Introduction to Physic:  This is a classic opening topic in any study of physics.

On this web site you may go to the page "What is physics" by clicking here

2. The Mathematics of Physics:  This is a necessary part of any beginning course.

As an example of such, go to the page "Physics Math Review" by clicking on this

3. Study of Motion (Kinematics) in a Straight Line:  Traditionally the study of physics involves a study of classical physics.  Classical physics "evolved" over the centuries, beginning historically with a combined study of astronomy and the motion of objects. Most courses in physics begin in the same way with the study of classical physics.  The study of motion focuses on displacement, velocity, and acceleration.

Link To The study of 1 Dimensional Kinematics: "1-D Kinematics"

4. Vectors:  Vectors is an area of measurement associated with mathematics and physics.  Measurements are categorized into scalar and vector quantities.  Most everyone in the course of their everyday life encounter and use scalar quantities.  Scalar quantities are measurements without any statement of direction.  As an example, a measurement of distance, such as 5.0 x 10^3 meters. is a scalar measurement.  On the other hand vector quantities have a direction associated with them.  As an example, a measurement of displacement, such as 5.0 x 10^3 meters north, is a vector measurement.

5. Using Mathematical Models to represent Motion:  When representing motion, experiments and observations provide data which allow for conclusions to be drawn based on patterns observed within the data.  These patterns can be observed through the processing of data in the form of graphs.  The analysis of graphed data often leads to conclusions that can be expressed in the form of mathematical equations.

6. The study of Forces (Dynamics):  The study of forces is a very important component of the study of physics.  The cornerstone of this study is Newton's three laws.

Newton's 1st Law:  "Every body [or object] continues in a state of rest or at a uniform speed [moving with constant velocity] in a straight line unless it is affected by an unbalanced force [net force > 0] causing it to experience acceleration, which results in a change in its motion."

Newton's 2nd Law:  "The acceleration of a body [or object] is directly proportional to [or varies directly with] an unbalanced force [a net force] acting on it and is inversely proportional to [varies inversely with] its mass.  The acceleration produced by an unbalanced force is in the same direction as the unbalanced force.  The equation expressing this law is  F = m a."

Newton's 3rd Law:  Whenever an object exerts a force on another object, the other object exerts a force equal and opposite in direction on the first object.

7. Forces and Motion in Two Dimensions:  Motion in two (and even three) dimensions is a  more complicated situation and requires using vector addition and subtraction to determine the outcome of combining multi-directional forces and their affects on motion.  A projectile being launched, an object moving in a circle, and a pendulum swinging back and forth are three examples of motion in two dimensions.

8. Universal Gravitation:  Keplers three laws of planetary motion are often introduced here. His three laws are:

Kepler's 1st Law:  The paths of planets are ellipses, with the sun at one focus.

Kepler's 2nd Law:  An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals.  Thus, planets move faster when they are closer to the sun and slower when they are farther away from the sun.

Kepler's 3rd Law:  The square of the ratios of the periods of any two planets revolving about the sun is equal to the cube of the ratio of their average distances from the sun.  The equation is written as (T1 / T2)^2 = (r1 / r2)^3

Newton studied Kepler's laws and deduced that the force of gravity acting on a planet due to the sun varies inversely with the square of the distance between the planet and  the sun.  Newton continued with his study and determined the equation to calculate the force of gravity between two objects, but could not determine the proportionality constant to use the equation.  Cavendish came along later and not only found that constant, but invented a device to measure the force of gravity between small objects in a laboratory.  (It is interesting at this point to compare Einstein's perception of gravity with that of Newton.)  The equation for his law of universal gravitation is  F(gravity) = G (m1 m2) / d^2

9. Momentum:  Newton wrote his three laws of motion in terms of momentum.  Momentum is the "quantity of motion" (Newton's definition).  When engineers plan for brake systems and engines on vehicles, they take into account not just the velocity range over which the vehicle is to operate, but combine that information with the mass of the vehicle to learn how much force is really necessary to accelerate and decelerate the vehicle within acceptable time intervals.  The subject of momentum is also an important tool in studying collisions and developing safety equipment for vehicles.  The law of conservation of momentum says that the momentum of any closed system with no external net forces does not change.  The equation for calculating momentum is  p = m v

10. Energy and Work:  Energy is sometimes described as the ability to do work.  Work is the product of force and distance.  The work-energy theorem says that when work is done on a body (or object) a change in the kinetic energy (the energy of motion) of the body occurs.  Power is the rate at which work is done.  Under this topic simple and compound machines are introduced. The six simple machines are the lever, the inclined plane, the pulley, the wheel and axle, the wedge, and the screw. The study of machines also includes the study of mechanical advantage and efficiency. The equations for work and power respectively are W = F d  and  P = W / t

11. Energy:  There are many kinds of energy.  The two general divisions of energy are the categories of potential and kinetic energy.  There are several kinds of energy, such as mechanical, chemical, nuclear, and gravitational.  Emphasis is usually on mechanical energy with the study of kinetic and gravitational potential energy.  Kinetic energy is the energy of motion.  If an object is in a state of motion it has both mass and velocity.  Gravitational potential energy is the energy of position.  An object at a greater height has more potential energy than an object which is closer to the ground.  The use of gravitational potential energy can be seen in the use of falling water to drive machinery such in hydro-electric dams.  The law of conservation of energy says that In a closed isolated system energy is neither created nor destroyed.  It only can change form.  The equations for kinetic and gravitational potential energy are respectively  KE = 1/2 m v^2  and  PE = m g h

12. The study of Thermal Energy (Thermodynamics):  Thermal energy is heat energy.  Temperature is a "tool" that allows the comparison of two temperatures, one being a reference temperature, on a relative scale invented by someone.  For example, Fahrenheit wanted a scale that would have the human body temperature at around 100 degrees.  He set the zero value on his scale to be the temperature of the coldest environment he could produce.  At that time that was the temperature of a salt water ice bath.  (Solutes lower the temperature at which water will freeze.)  It turns out that average human body temperature is 98.6 degrees on his scale and water boils at 212 degrees on his scale.  Celsius had a different set of references for defining his scale.  He chose the freezing and boiling points of pure water to define his 0 degree and 100 degree marks respectively.  He thought it was more efficient to have 100 divisions between the freezing point and boiling points of water as compared to the 180 degree difference on the Fahrenheit scale.  Today, in science, the preferred scale is the Kelvin scale.

While determining the exact total amount of heat energy contained within an object may be extremely challenging, determining the amount of heat gained or lost by a substance is not.  The mass of a substance, its specific heat, and its temperature change are all that is needed to calculate the amount of heat transferred to or from the substance.  The equation for determining the amount of heat gained or lost by a substance when it remains in the same state (solid, liquid, or gas) is  Q = m c /\ T

Determining the amount of heat gained or lost during a melting / freezing process  respectively can be done when the mass of the substance and its heat of fusion are known.  The equation used is Q = m H(f)

Determining the amount of heat gained or lost during a boiling / condensing process respectively can be done when the mass of the substance and its heat of vaporization are known.  The equation used is  Q = m H(v)

13. States of Matter:  There are three states of matter explored at this level.  They are the solid, liquid, and gaseous states.  Solids have the characteristics of definite shape and volume in addition to a list of properties associated with solid material, such as hardness, malleability, ductility, and so on.  Liquids have no definite shape, taking the shape of the container, but do have definite volume.  Gases have no definite shape or volume having to be confined to a closed container where they expand to fill the container taking the shape of the container.  Liquids and gases have similar characteristics and are called fluids.

Fluids are materials that flow and have no definite shape.  Pressure affects fluids.  Pressure is the force on a surface divided by the area of the surface.  All material on the surface of the earth experience the pressure of the atmosphere pushing on them.  Atmospheric pressure at sea level is about 14.7 pounds per square inch.  The equation for pressure is  P = F / A

Fluid characteristics have resulted in some interesting discoveries.

• Pascal's Principle:  Any change in pressure applied at any point on a confined fluid is transmitted undiminished throughout the fluid.
• Archimedes' Principle:  An object immersed in a fluid has an upward force on it equal to the weight of the fluid displaced by the object.
• Bernoulli's Principle:  As the velocity of a fluid increases, the pressure exerted by that fluid decreases.
Thermal Expansion of Matter:  Temperature changes affect the volume of solids, liquids, and gases.  Thermal expansion of solids and liquids is based upon values called thermal expansion coefficients.  These values allow for the calculation of change in volume in an object as heat is transferred to or from the object.  Change in volume of gases is described in terms of the gas laws.

The Gas Laws are:

• Boyle's Law:  At constant temperature, the pressure and volume of a gas are inversely proportional to one another.
• Charles' Law:  At constant pressure, the temperature and volume of a gas are directly proportional to one another.
• Gay-Lussac's Law:  At constant volume, the temperature and pressure of a gas are directly proportional to one another.
• The Combined Gas Law:  This law is a combination of the first three laws and is often expressed as  "The multiplication product of pressure and volume of a gas is proportional to the temperature of the gas."
• The Ideal Gas Law:  This law merges the measure of the quantity of gas present into the Combined Gas law.  The law can be expressed as "The multiplication product of the pressure and volume of a gas is proportional to the multiplication product of the number of moles and the temperature of the gas."

14. Wave Phenomena:  Energy can be transferred through the transmission of waves.  Waves rolling up on the shore are a good example of this.  Energy is being transferred to the shore and can be powerful enough to knock a person or even a building down as well as cause varying degrees of erosion.  Sound and Light (electromagnetic waves) are two very important categories of wave phenomena.  Frequency, wavelength, speed, and amplitude are characteristics common to all forms of waves, including sound and light.

Comparison of sound and light:

 Sound Light Frequency Pitch Color Amplitude Loudness Brightness

Wave Behavior:  Waves exhibit certain behaviors when encountering matter.  Three important properties of waves are reflection, refraction, and diffraction.  Each is briefly described below.

The Law of Reflection:  When a wave strikes a boundary where two media like air and glass meet some of the energy is reflected and some is transmitted or absorbed.  The portion of the wave that is reflected is reflected according to the law of reflection.  This law says "The angle of reflection is equal to the angle of incidence.".

Refraction:  When a wave strikes a boundary where two media like air and glass meet some of the energy is reflected and some is transmitted or absorbed.  The portion of the wave that crosses the boundary is called the transmitted wave.  When it crosses into the new medium its velocity changes.  This results in the transmitted wave changing direction.  This changing of velocity resulting in the bending of a light wave as it crosses the boundary between two media is called refraction.

Diffraction:  Waves spread out as they travel.  When they encounter a barrier, they bend around its edges and pass into the area behind the barrier.  This bending of light waves around the edge of a barrier is called diffraction.

Optics:  Mirrors and lenses are used to focus light.  Real and virtual images are the result of certain mirrors and lenses affecting light.  In astronomy telescopes that use visible light are designed to take advantage of the properties of mirrors and lenses.  Refractor telescopes use lenses only to focus light.  Reflector telescopes use a combination of mirrors and lenses to focus light.  Corrective eye glasses, contact lenses, and light microscopes are some other areas dependent upon the study of optics.

15. Static Electricity, Electrical Current, and Magnetism:  The study of electricity involves the study of electrical charge.  Static electricity focuses on stationary charges.  Electric current focus on moving charges.  Below are several important concepts associated with the study of electricity.

Coulomb's Law:  The magnitude of the force between charge q1 and charge q2 separated by a distance d, is proportional to the magnitude of the charges and inversely proportional to the square of the distance.  The Equation is  F = K q1 q2 / d^2

Electric field:  The electric field is a vector quantity that relates the force exerted on a test charge to the size of the test charge.  The Equation is  E = F / q

Electric Potential Difference:  The electric potential difference is the work done moving a test charge in an electric field divided by the magnitude of the test charge.  The Equation is  /\V = W / q

Capacitance:  When a charge is added to an object the electric potential difference between the object and the earth is increased.  Capacitance is the ratio of charge stored to electrical potential difference.  The Equation is  C = q / /\V

Electric Current:  Electric current is the flow of charged particles from an area or source rich in electrical charge to an area or location poor in charge.  In the case of a simple flashlight circuit one terminal of the battery is electron rich and the other is electron poor.  When the switch is engaged (closed or in the on position) electrons are free to move through the path (circuit) from the negative terminal to the positive terminal.  This flow is called electricity or electrical current.  Historically, before the subatomic particle called the electron was known, electricity was defined as the flow of positive charge.  Electricity can be described as the flow of positive charge and this flow is in the opposite direction to the flow of electrons.  The flow of positive charge is called conventional current.

Electric Power:  Power was defined earlier in mechanical terms as the amount of work done per unit of time.  The movement of electrical charge also involves power.  The power, or energy delivered to an electrical device per second can be found by multiplying the current flowing through a circuit by the voltage applied to the circuit through which the current is flowing.  The Equation is  P = V I

Ohm's law:  The property of a material, like a piece of metal, that determines how much electricity will flow through it is called electrical resistance.  The symbol for electrical resistance is an upper case R.  The equation is  R = V / I

Electrical Circuits:  The paths that electricity follows are called circuits.  They range from the very simple single path with one resistance to more complex paths involving more than one resistance and multiple paths.  As an example of how complex a circuit could be take a quick look at a circuit diagram of some appliance you have in your home.  Often such a diagram is in the owners manual depending on the type of appliance.

The two major categories of circuits are the series circuit and the parallel circuit.  The series circuit has all resistances whether they be light bulbs or something else connected together in a single path. Often the cheapest christmas tree light strings are of this type where one bulb goes out in the circuit and they all quit because they are attached in a string where the current has been interrupted by the burned out, broken, or missing bulb.  There are uses for series circuits such as in multiple battery flashlights and some short secondary paths in a more complex appliance circuit, but in general parallel circuits are preferred so if one bulb or appliance quits all the other electrical devices remain on.  The wiring in buildings is down as parallel circuits which is why there are so many fuses or circuit breakers in the main electrical box.

Magnetism:  Magnetism has always been a curious sort of phenomenon.  It took a very long time for humans to recognize what magnetism is and discover the connection between electricity and magnetism.  In fact today the two could be considered as two sides of the same coin called electro-magnetism.  Only a few materials display significant natural magnetism.  These materials are described as being ferromagnetic.  Other materials show very slight magnetic effects only detectable with very sensitive instruments.  Ferromagnetic materials are mad up of small regions on the size of a millimeter across called domains.  Each domain is itself a tiny magnet.  If the domains in a piece of ferromagnetic material, the entire piece of material acts as a magnet.  If the domains are randomly arranged they are likely to have canceled each others magnetism out, and the entire piece of material does not exhibit any significant magnetism.  Banging a magnet or heating it can cause the domains to move out of alignment causing the magnetism to be diminished or lost entirely.  It is the electron spin in the atoms making up the domains that is believed to be the cause of the magnetism.  Only in a few elements do the atom's electrons' spin add up.  In most elements they cancel each other out.  These few that do are the ferromagnetic elements.

Electro-Magnetism:  As electric charge moves, such as electrons flowing through a copper wire in a circuit, they produce a magnetic field around them and thus around the wire.  This is easily observed by bringing a small compass near a wire through which a current is flowing.  The needle will line up in the direction of the magnetic field.  Likewise, if a wire is moved in a magnetic field and it is part of a loop (or circuit) an electric current will flow through the wire.  These two phenomena are used in electric motors and electric generators respectively.

16. Atomic Theory and Nuclear Processes:  Though the structure of the atom is quite complex, looking it from the point of view of the early part of the 20th century, which is traditionally used in many K-12 science classes, the atom can be explained according to the Bohr model of the atom.  Essentially the atom has a very small dense center called the nucleus.  The nucleus is about 1 / 10,000 the diameter of the entire atom and contains 99+ % of the mass of the atom.  Within the nucleus are found the protons and the neutrons.  Outside the nucleus are found the electrons.  In the table below a few facts about these particles are summarized.

 Symbol Charge Mass (kg) Location Protons p+ +1 1.6726 x 10^-27 nucleus Neutrons no 0 1.6749 x 10^-27 nucleus Electrons e- -1 9.11 x 10^-31 Outside nucleus in shells or E.L.*
* E.L. = energy levels

Atomic Spectra:  When an atom is excited, that is, energy is added, the electrons jump to higher levels.  When they fall back they give off emission spectra that can be used to identify the material whose atoms are being excited.  The patterns of lines of light emitted are like finger prints.  When an unidentified substance such as at a crime scene is submitted to spectral analysis, the spectral lines produced are compared to known spectral lines until a match is made.

Quantum Model of the Atom:  As the twentieth century unfolded, the quantum model of the atom evolved.  The model says that there is a wave particle nature to matter and it is impossible to know both the position and the momentum of an electron at the same time.  The model predicts the probability of an electron being in a specific location.  It does predict that the most likely place to find an electron in the hydrogen atom is the same as the radius of the electron orbit in the Bohr model of the hydrogen atom.  The probabilities of an electron being at different radii can be calculated and translated into a three dimensional model.  The region with the highest probability is called the electron cloud.

Nuclear Processes:  The nucleus of the atom was probed throughout much of the twentieth century.  The first successful nuclear fission reactor was built and operated in a bunker built under football field stadium in the early 1940's at the University of Chicago.  This experiment was part of the Manhattan Project to develop an atomic bomb.

Natural Radioactivity:  The number of protons in a nucleus determine what element the atom belongs to.  The number of neutrons in an atom defines which isotope the atom is among the isotopes of the element.  When there is an imbalance of neutrons to protons in the nucleus of an atom, the atom will give off some form of radiation to reduce its instability.  Below is a table describing three common forms of radiation.

 Name Symbol Composition Category Alpha a 1 He nucleus particle Beta (minus) b- 1 electron particle Gamma g Electromagnetic Radiation energy

Nuclear Fission:  This process involves fissioning (splitting apart) atoms of a fissionable material.  The classic (well Known) fission reaction involves a neutron colliding with an isotope of uranium which splits into an isotope of Barium and an isotope of Krypton.  In the process energy is released along with 2-3 more neutrons.  Today's nuclear reactors, whose heat is used to boil steam to run the turbines that turn the electrical generators, use fission.

Nuclear Fusion:  This process involves fusing (putting together) small atoms and combining them into larger ones.  The process is of the type that takes place in stars like our own sun.  Smaller hydrogen nuclei are fused in to larger, heavier helium nuclei.  Within stars that are "dying", running out out of hydrogen, the fusion process will shift to the fusing Helium to make Lithium and so on as the fusion of heavier elements occurs.  The process keeps the star going for a longer period of time.  Efforts to use the fusion process in nuclear reactors is at the experimental stage.

From Einstein to the Present:  The physics of the twentieth century is immense as compared to all of the science that preceded it.  Studying that era of physics is another long and fascinating journey.  Use web sites, libraries, and other sources as you find time to pursue it.