Kinematics
Kinematics is the study of motion and strain in bodies without reference to the forces that effect
them.
Dynamics
Dynamics is the study of forces that effect the motion and strain in bodies. It is divided into two
categories, statics and kinetics.
Statics is a study of bodies in equilibrium or when all the forces effecting a body neutralize each
other. When a body is not changing relative position, it is in equilibrium.
Kinetics is a study of forces that change the motions of bodies. When a body is changing relative
position, it is in motion.
Displacement
Displacement is the measurement between two points. The position of a point is relatve to the
displacement of another point.
Buoyancy
Buoyancy is a measure of upward force. The net upward force is equal to the weight of fluid or gas
displaced by a body. A body's buoyancy in water depends on its density and displacement volume.
One cubic foot of water has a density ratio of 1. Solid bodies that have a density ratio of less than
1
will float in water. Solid bodies with a density ratio greater the 1 will sink.
A hollow body (such as metal boats) which has a density ration greater than 1 will float if it
displaces a volume of water that is greater than its own weight.
A hollow body that contains or supports solid bodies will not sink if their combine weight is less
than the weight of the water volume that it displaces .
Inertia
Inertia is a measure of resistance to change motion. A body resists changes in momentum, speed,
acceleration, and direction.
Moment of Inertia
Moment of inertia is a measure of resistance to change in angular motion. A body resists changes in
rotational or angular speed and acceleration.
Momentum
Momentum is a measure of a body's impact, impulse or motion. A body's momentum is determined
by its mass and speed. Speed is a change in a body's position relative to other bodies over time. A
body's position relative to other bodies is called distance.
Kinetic Energy
Kinetic energy is a measure of a body's energy in motion. A body's kinetic energy is determined by
its momemtum and average change in positions relative to other bodies over time. A body's position
relative to other bodies is called distance. The average change in a body's distance relative to other
bodies over time is called average speed.
Potential Energy
Potential energy is a measure of a body's energy in position. A body's potential energy is
determined by its position and acceleration relative to other bodies and its mass. A body's position
relative other bodies is called distance.
Gravity
Gravity is the attractive forces between bodies in motion. It is created by a body's change in speed
or mass relative to other bodies. A change in speed is called acceleration.
A collection of bodies in motion is called a field. The attractive forces between these bodies is
called a gravity field. A change in mass or acceleration of a single body will change the strength of
the gravity field.
Moment or Torque
A moment or torque is a product of force and armdistance about a point or center. The force is
perpendicular to the armdistance. An object bends or rotates when a moment or torque is applied
to it.
Elasticity
Elasticity is a measure of a body's flexibility. It is the ratio of stress to strain. When an external
force
changes an object's shape and size, it is said to be under stress, and the accompanying distortion or
change in volume or length is called strain.
In bodies which are homogeneous and isotropic there are two kinds of elasticity, volume and
rigidity. Volume elasticity is measured in pressure per change in unit volume. Rigidity is measured
in
compression or tension per change in unit length.
Stress
Stress is a measure of force per unit surface (as in grams per square centimeter). If it stretches a
body, it is called shear, tension or tensile stress. If it shortens a body, it is call pressure,
compression or compressive stress.
Strain
Strain is a measure of resistance to external forces. It is the ratio of displacement or deformation
to original unit length or volume (as in displacement per original length). It may be tensile,
compressive, or shear. Displacement or deformatrion is the difference between orginal length or
volume and the new length or volume.
Work, Energy, Power
Work is the amount force used to move an object (motion).
Energy is the amount of Work used over a period of time.
Power is the amount of Energy used over a period of time.
A Grammeter is a unit of work.
A Joule is a unit of energy.
A Watt is a unit of power.
One Joule is
A 2 Liter soda bottle falling over.
A cubic centimeter of water falling 100 meters (330 feet).
The kinetic energy of a crawling baby.
You slowly swaying.
A clapping hand.
1 kilogram moving at 1.5 meter/second.
2 kilogram moving at 1 meter/second. (slowly pushing a 2L soda bottle)
One second of sunlight on a 10 cm square patch of ground.
The snap of rubber band.
Joules are used to calculate power (the flow of energy over time in Wattshours).
1. kilojoule (kJ)  a small 13 watt compactflourescent bulb uses up 1 kJ in 1000/13 = 76 seconds.
2. megajoule (MJ)  one kilowatthour (kWh) is 3.6 MJ per hour. Or, four 75 watt light bulbs use
MJ per hour
Irration Numbers
There are three constant in mathematics,
epsilon (e) = 2.718... non repeating to infinity
pi = 3.141... non repeating to infinity
phi = 1.618... non repeating to infinity
All three constants are irrational numbers. An irrational number is simply a number that cannot be
written as a fraction.
e and pi are transcendental numbers. A transcendental number is a real number that is not the
solution of any singlevariable polynomial equation whose coefficients are all integers.
pi is the ratio of a curve's length to the distance between two points on the curve. The curve can be
a spiral, a winding road or a circle. It is a transcendental number found in nature.
Like pi, e is a transcendental number. It shows up whenever physical systems of nature grow
exponentially and continuously: population, radioactive decay, interest rate calculations, and more.
Even jagged systems that don’t grow smoothly can be approximated by e. It is used as a natural
base logarithm. A logarithm is the power to which a number must be raised in order to get some
other number. For example, the base 10 logarithm of 100 is 2, because ten raised to the power of 2
is 100: log 100.
phi is a special number found by dividing a line into two parts so that the longer part divided by the
smaller part is also equal to the whole length divided by the longer part. It is also the solution to
a
singlevariable polynomial whose coefficient is an integer. As with pi, the digits go on and on,
theoretically into infinity. It appears in all forms of nature and science. Some include: Flower petals,
Seed heads, Tree branches, the curve of a Nautilus
shell, Hurricanes, your fingers and DNA.
Fast Fourier and Laplace Transforms
What are they?
In system engineering, there are two important transforms, Fast Fourier and Laplace. Fast Fourier
transform is a tool for signal processing and Laplace is mainly applied to circuit analysis controller
design.
What do they do?
Many of the parameters in our universe interact through differential equations. For example, the
voltage across an inductor is proportional to the derivative of the current through the device.
Likewise, the force applied to a mass is proportional to the derivative of its velocity.
Fast Fourier and Laplace transforms analyze differential equations.
How do they work?
Laplace transform maps a system's differential equation onto a linear algebraic equation.
That equation is solved.
The solution of the algebraic equation is mapped back onto the solution of the given differential
equation.
Fast Fourier transform converts a signal from its original domain (often time and space) to a
representation in the frequency domain and vice versa.
Applications:
Fast Fourier transform is used:
to detect seizure problems in EEG electrical signals,
to convert 3D images into electrical signals,
to convert electrical signals into 3D images for analysis.
Laplace transform is used to solve analysis problems in electrical circuits (often filters).
Gravity
Gravity is a diverse resource of infinite elements. It is in a constant state of flux, always becoming
and never is. It permeates, penetrates, and fills the interspace of the universe.
Every element is connected to every other element.
Every element has a collateral effect on every other element.
Every element is related to every other element.
Every element is constantly being rearranged, combined and transformed into an infinite number of
substances by a continuum of interactions with spacetime, energymatter and momentumposition.
Baryon Particles
Baryon particles have three quarks (qqq). They are the building blocks of atoms, neutrons and
protons. A proton has two up and one down quark (uud) and a neutron has two down quarks and
one up quark (ddu).
The proton is the only stable baryon all other baryons eventually decay into a proton. Neutrons and
protons are held together by a strong nuclear force to form a nucleus. The strong nuclear force acts
over a very short range. It can be both attractive & repulsive.
All nuclei with more than 83 protons are unstable and radioactive. Radioactive nuclei emit: alpha
particles (2 protons and 2 neutrons, helium nucleus), beta particles (high speed electron), and
gamma rays (a photon).
An alpha particle is produced when an unstable nucleus emits a positive charged nucleus (helium).
Subsequent to its emission, the particle attracts electrons from other nuclei.
A beta particle is produced when a neutron decays into a proton and some of its mass is converted
into high energy electrons.
A gamma ray is produce when an unstable nucleus loses energy in the form of a photon (a very
short electromagnetic wavelength). It is analogous to an electron transitioning from a high energy
state to a low energy state.
Radiation shielding is based on the principle of attenuation, which is the ability to reduce a particle
or ray’s effect by absorption through a barrier material.
Alpha radiation can be stopped after traveling through about 1.2 inches of air, about 0.008 inches
of water, or a piece of paper or skin. However, living tissue inside the body offers no protection
against inhaled or ingested alpha emitters.
Beta radiation can only be stopped after traveling through about 10 feet of air, less than 2 inches
of
water, or a thin layer of glass or metal. Additional covering, for example heavy clothing, is
necessary to protect against beta emitters. Some beta particles can penetrate and burn the skin.
Gamma radiation can be reduce after traveling through about 13.8 feet of water, about 6.6 feet of
concrete, or about 1.3 feet of lead. Thick, dense shielding is necessary to protect against gamma
rays. The higher the energy of the gamma ray, the thicker the shield must be.
Photons
A Photon is a packet of electromagnetic energy waves. Its power is measured in (joules per second
or watts) and is dependent on frequency or wavelength. Low power photons (radio and infrared
waves) have a longer wavelength than high power photons (microwave, visible light, ultraviolet light,
gamma and xrays).
Photon intensity is the number photons passing through or striking a square area (joules per square
area). Increasing the intensity raises the energy level but not the power. This is analogous to using
a
magnifying glass to focus the sun's energy on a fixed square area in space. The energy level per
square area will rise but the power remains constant.
The energy level of electrons become unstable when they interact with photons and emit photons
when they decay to a stable level.
Protons become unstable neutrons when they interact with photons. Unstable neutrons emit high
speed photons and electrons when they decay to stable protons.
Like gravity, photons (electromagnetic energy) permeate, penetrate and fill the interspace of
everything. They are the yin and yang of the universe. Gravity and photons occupy the same space
in time. The interaction between gravity and photons creates a continuum of energymatter, spacetime
and momentumposition.
The energymatter continuum is a transition carrier for photons (electromagnetic energy) and matter.
Some photons transitions into stable and semistable elements. Gravity combines these elements to
create hadron particles and leptons, the basic building blocks of matter. Some matter transitions into
photons and semistable matter.
The spacetime continuum is a transition carrier for expanding matter. The momentumposition
continuum is a transition carrier for changing the momentum and position of matter.
Gravity, photons (electromagnetic energy), energymatter, spacetime and the momentposition
continuum connect everything to everything. This makes everything relative to everything and
everything has a collateral effect on everything else.
Gravity, photons (electromagnetic energy), energymatter, spacetime and the momentposition
continuum connect everything to everything. Everything is relative to everything and everything has
a
collateral effect on everything.
