Classical mechanics is the branch of physics that describes the motion of macroscopic objects. It is based on Newton's laws of motion and law of universal gravitation. Classical mechanics provides accurate results for large objects moving at non-relativistic speeds. When dealing with very small objects or speeds approaching the speed of light, quantum mechanics and special relativity are required. Classical mechanics includes formulations like Lagrangian and Hamiltonian mechanics that extend Newton's original work.

1. Physics (from Ancient Greek: φύσις physis "nature") is a natural science that involves the study
of matter[1] and its motion through space and time, along with related concepts such as energy
and force.[2] More broadly, it is the general analysis of nature, conducted in order to understand
how the universe behaves.[3][4][5]
Science (from Latin scientia, meaning "knowledge") is a systematic enterprise that builds and organizes
knowledge in the form of testable explanations and predictions about the universe.[1] In an older and
closely related meaning (found, for example, in Aristotle), "science" refers to the body of reliable
knowledge itself, of the type that can be logically and rationally explained (see History and philosophy
below).[2] Since classical antiquity science as a type of knowledge was closely linked to philosophy. In the
early modern era the words "science" and "philosophy" were sometimes used interchangeably in the
English language. By the 17th century, natural philosophy (which is today called "natural science") was
considered a separate branch of philosophy.[3] However, "science" continued to be used in a broad
sense denoting reliable knowledge about a topic, in the same way it is still used in modern terms such as
library science or political science.
The branches of science (which are also referred to as "sciences", "scientific fields", or "scientific
disciplines") are commonly divided into two major groups: natural sciences, which study natural
phenomena (including biological life), and social sciences, which study human behavior and societies.
These groupings are empirical sciences, which means the knowledge must be based on observable
phenomena and capable of being tested for its validity by other researchers working under the same
conditions.[1] There are also related disciplines that are grouped into interdisciplinary and applied
sciences, such as engineering and medicine. Within these categories are specialized scientific fields that
can include parts of other scientific disciplines but often possess their own terminology and expertise.[2]
PHYSICS
Physics is the science of matter and energy, and the movement and interactions between them
both.
The most popular branches of physics are:
mechanics
electromagnetism
heat and thermodynamics
atomic theory
relativity
astrophysics
theoretical physics
optics, geophysics
biophysics
particle physics
sound
light
atomic and molecular physics

2. nuclear physics
solid state physics
plasma physics
geophysics
biophysics
The two main branches are : 1) Classical Mechanics 2) Quantum MechanicsThis article is about the
physics sub-field. For the book written by Herbert Goldstein and others, see Classical Mechanics
(book).
Classical mechanics
History of classical mechanics
Timeline of classical mechanics
Branches[show]
Formulations[show]
Fundamental concepts[show]
Core topics[show]
Scientists[show]
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In physics, classical mechanics is one of the two major sub-fields of mechanics, which is
concerned with the set of physical laws describing the motion of bodies under the action of a
system of forces. The study of the motion of bodies is an ancient one, making classical
mechanics one of the oldest and largest subjects in science, engineering and technology.
Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of
machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies.
Besides this, many specializations within the subject deal with gases, liquids, solids, and other
specific sub-topics. Classical mechanics provides extremely accurate results as long as the
domain of study is restricted to large objects and the speeds involved do not approach the speed
of light. When the objects being dealt with become sufficiently small, it becomes necessary to

3. introduce the other major sub-field of mechanics, quantum mechanics, which reconciles the
macroscopic laws of physics with the atomic nature of matter and handles the wave–particle
duality of atoms and molecules. In the case of high velocity objects approaching the speed of
light, classical mechanics is enhanced by special relativity. General relativity unifies special
relativity with Newton's law of universal gravitation, allowing physicists to handle gravitation at
a deeper level.
The term classical mechanics was coined in the early 20th century to describe the system of
physics begun by Isaac Newton and many contemporary 17th century natural philosophers,
building upon the earlier astronomical theories of Johannes Kepler, which in turn were based on
the precise observations of Tycho Brahe and the studies of terrestrial projectile motion of
Galileo. Since these aspects of physics were developed long before the emergence of quantum
physics and relativity, some sources exclude Einstein's theory of relativity from this category.
However, a number of modern sources do include relativistic mechanics, which in their view
represents classical mechanics in its most developed and most accurate form.[note 1]
The initial stage in the development of classical mechanics is often referred to as Newtonian
mechanics, and is associated with the physical concepts employed by and the mathematical
methods invented by Newton himself, in parallel with Leibniz, and others. This is further
described in the following sections. Later, more abstract and general methods were developed,
leading to reformulations of classical mechanics known as Lagrangian mechanics and
Hamiltonian mechanics. These advances were largely made in the 18th and 19th centuries, and
they extend substantially beyond Newton's work, particularly through their use of analytical
mechanics. Ultimately, the mathematics developed for these were central to the creation of
quantum mechanics.
Contents
1 History
2 Description of the theory
o 2.1 Position and its derivatives
 2.1.1 Velocity and speed
 2.1.2 Acceleration
 2.1.3 Frames of reference
o 2.2 Forces; Newton's second law
o 2.3 Work and energy
o 2.4 Beyond Newton's laws
3 Limits of validity
o 3.1 The Newtonian approximation to special relativity
o 3.2 The classical approximation to quantum mechanics
4 Branches
5 See also
6 Notes
7 References
8 Further reading

4. 9 External links
History
Main article: History of classical mechanics
See also: Timeline of classical mechanics
Classical Physics
Wave equation
History of physics
Founders[show]
Branches[show]
Scientists[show]
v
t
e
Some Greek philosophers of antiquity, among them Aristotle, founder of Aristotelian physics,
may have been the first to maintain the idea that "everything happens for a reason" and that
theoretical principles can assist in the understanding of nature. While to a modern reader, many
of these preserved ideas come forth as eminently reasonable, there is a conspicuous lack of both
mathematical theory and controlled experiment, as we know it. These both turned out to be
decisive factors in forming modern science, and they started out with classical mechanics.
The medieval "science of weights" (i.e., mechanics) owes much of its importance to the work of
Jordanus de Nemore. In the Elementa super demonstrationem ponderum, he introduces the
concept of "positional gravity" and the use of component forces.

5. Three stage Theory of impetus according to Albert of Saxony.
The first published causal explanation of the motions of planets was Johannes Kepler's
Astronomia nova published in 1609. He concluded, based on Tycho Brahe's observations of the
orbit of Mars, that the orbits were ellipses. This break with ancient thought was happening
around the same time that Galileo was proposing abstract mathematical laws for the motion of
objects. He may (or may not) have performed the famous experiment of dropping two cannon
balls of different weights from the tower of Pisa, showing that they both hit the ground at the
same time. The reality of this experiment is disputed, but, more importantly, he did carry out
quantitative experiments by rolling balls on an inclined plane. His theory of accelerated motion
derived from the results of such experiments, and forms a cornerstone of classical mechanics.
Sir Isaac Newton (1643–1727), an influential figure in the history of physics and whose three
laws of motion form the basis of classical mechanics
As foundation for his principles of natural philosophy, Isaac Newton proposed three laws of
motion: the law of inertia, his second law of acceleration (mentioned above), and the law of

6. action and reaction; and hence laid the foundations for classical mechanics. Both Newton's
second and third laws were given proper scientific and mathematical treatment in Newton's
Philosophiæ Naturalis Principia Mathematica, which distinguishes them from earlier attempts at
explaining similar phenomena, which were either incomplete, incorrect, or given little accurate
mathematical expression. Newton also enunciated the principles of conservation of momentum
and angular momentum. In mechanics, Newton was also the first to provide the first correct
scientific and mathematical formulation of gravity in Newton's law of universal gravitation. The
combination of Newton's laws of motion and gravitation provide the fullest and most accurate
description of classical mechanics. He demonstrated that these laws apply to everyday objects as
well as to celestial objects. In particular, he obtained a theoretical explanation of Kepler's laws of
motion of the planets.
Newton previously invented the calculus, of mathematics, and used it to perform the
mathematical calculations. For acceptability, his book, the Principia, was formulated entirely in
terms of the long-established geometric methods, which were soon to be eclipsed by his calculus.
However it was Leibniz who developed the notation of the derivative and integral preferred[citation
needed]
today.
Hamilton's greatest contribution is perhaps the reformulation of Newtonian mechanics, now
called Hamiltonian mechanics.
Newton, and most of his contemporaries, with the notable exception of Huygens, worked on the
assumption that classical mechanics would be able to explain all phenomena, including light, in
the form of geometric optics. Even when discovering the so-called Newton's rings (a wave
interference phenomenon) his explanation remained with his own corpuscular theory of light.
After Newton, classical mechanics became a principal field of study in mathematics as well as
physics. After Newton there were several re-formulations which progressively allowed a solution
to be found to a far greater number of problems. The first notable re-formulation was in 1788 by
Joseph Louis Lagrange. Lagrangian mechanics was in turn re-formulated in 1833 by William
Rowan Hamilton.

7. Some difficulties were discovered in the late 19th century that could only be resolved by more
modern physics. Some of these difficulties related to compatibility with electromagnetic theory,
and the famous Michelson–Morley experiment. The resolution of these problems led to the
special theory of relativity, often included in the term classical mechanics.
A second set of difficulties were related to thermodynamics. When combined with
thermodynamics, classical mechanics leads to the Gibbs paradox of classical statistical
mechanics, in which entropy is not a well-defined quantity. Black-body radiation was not
explained without the introduction of quanta. As experiments reached the atomic level, classical
mechanics failed to explain, even approximately, such basic things as the energy levels and sizes
of atoms and the photo-electric effect. The effort at resolving these problems led to the
development of quantum mechanics.
Since the end of the 20th century, the place of classical mechanics in physics has been no longer
that of an independent theory. Instead, classical mechanics is now considered to be an
approximate theory to the more general quantum mechanics. Emphasis has shifted to
understanding the fundamental forces of nature as in the Standard model and its more modern
extensions into a unified theory of everything.[1] Classical mechanics is a theory for the study of
the motion of non-quantum mechanical, low-energy particles in weak gravitational fields. In the
21st century classical mechanics has been extended into the complex domain and complex
classical mechanics exhibits behaviors very similar to quantum mechanics.[2]
Description of the theory
The analysis of projectile motion is a part of classical mechanics.
The following introduces the basic concepts of classical mechanics. For simplicity, it often
models real-world objects as point particles, objects with negligible size. The motion of a point
particle is characterized by a small number of parameters: its position, mass, and the forces
applied to it. Each of these parameters is discussed in turn.
In reality, the kind of objects that classical mechanics can describe always have a non-zero size.
(The physics of very small particles, such as the electron, is more accurately described by

8. quantum mechanics). Objects with non-zero size have more complicated behavior than
hypothetical point particles, because of the additional degrees of freedom—for example, a
baseball can spin while it is moving. However, the results for point particles can be used to study
such objects by treating them as composite objects, made up of a large number of interacting
point particles. The center of mass of a composite object behaves like a point particle.
Position and its derivatives
Main article: Kinematics
The SI derived "mechanical"
(that is, not electromagnetic or thermal)
units with kg, m and s
position m
angular position/angle unitless (radian)
velocity m·s−1
angular velocity s−1
acceleration m·s−2
angular acceleration s−2
jerk m·s−3
"angular jerk" s−3
specific energy m2·s−2
absorbed dose rate m2·s−3
moment of inertia kg·m2
momentum kg·m·s−1
angular momentum kg·m2·s−1
force kg·m·s−2
torque kg·m2·s−2

9. energy kg·m2·s−2
power kg·m2·s−3
pressure and energy density kg·m−1·s−2
surface tension kg·s−2
spring constant kg·s−2
irradiance and energy flux kg·s−3
kinematic viscosity m2·s−1
dynamic viscosity kg·m−1·s−1
density (mass density) kg·m−3
density (weight density) kg·m−2·s−2
number density m−3
action kg·m2·s−1
The position of a point particle is defined with respect to an arbitrary fixed reference point, O, in
space, usually accompanied by a coordinate system, with the reference point located at the origin
of the coordinate system. It is defined as the vector r from O to the particle. In general, the point
particle need not be stationary relative to O, so r is a function of t, the time elapsed since an
arbitrary initial time. In pre-Einstein relativity (known as Galilean relativity), time is considered
an absolute, i.e., the time interval between any given pair of events is the same for all observers.
In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the
structure of space.[3]
Velocity and speed
Main articles: Velocity and speed
The velocity, or the rate of change of position with time, is defined as the derivative of the
position with respect to time or
.

10. In classical mechanics, velocities are directly additive and subtractive. For example, if one car
traveling east at 60 km/h passes another car traveling east at 50 km/h, then from the perspective
of the slower car, the faster car is traveling east at 60 − 50 = 10 km/h. Whereas, from the
perspective of the faster car, the slower car is moving 10 km/h to the west. Velocities are directly
additive as vector quantities; they must be dealt with using vector analysis.
Mathematically, if the velocity of the first object in the previous discussion is denoted by the
vector u = ud and the velocity of the second object by the vector v = ve, where u is the speed of
the first object, v is the speed of the second object, and d and e are unit vectors in the directions
of motion of each particle respectively, then the velocity of the first object as seen by the second
object is
Similarly,
When both objects are moving in the same direction, this equation can be simplified to
Or, by ignoring direction, the difference can be given in terms of speed only:
Acceleration
Main article: Acceleration
The acceleration, or rate of change of velocity, is the derivative of the velocity with respect to
time (the second derivative of the position with respect to time) or
Acceleration can arise from a change with time of the magnitude of the velocity or of the
direction of the velocity or both. If only the magnitude v of the velocity decreases, this is
sometimes referred to as deceleration, but generally any change in the velocity with time,
including deceleration, is simply referred to as acceleration.
Frames of reference
Main articles: Inertial frame of reference and Galilean transformation

11. While the position and velocity and acceleration of a particle can be referred to any observer in
any state of motion, classical mechanics assumes the existence of a special family of reference
frames in terms of which the mechanical laws of nature take a comparatively simple form. These
special reference frames are called inertial frames. An inertial frame is such that when an object
without any force interactions (an idealized situation) is viewed from it, it will appear either to be
at rest or in a state of uniform motion in a straight line. This is the fundamental definition of an
inertial frame. They are characterized by the requirement that all forces entering the observer's
physical laws originate in identifiable sources (charges, gravitational bodies, and so forth). A
non-inertial reference frame is one accelerating with respect to an inertial one, and in such a non-
inertial frame a particle is subject to acceleration by fictitious forces that enter the equations of
motion solely as a result of its accelerated motion, and do not originate in identifiable sources.
These fictitious forces are in addition to the real forces recognized in an inertial frame. A key
concept of inertial frames is the method for identifying them. For practical purposes, reference
frames that are unaccelerated with respect to the distant stars are regarded as good
approximations to inertial frames.
Consider two reference frames S and S'. For observers in each of the reference frames an event
has space-time coordinates of (x,y,z,t) in frame S and (x',y',z',t') in frame S'. Assuming time is
measured the same in all reference frames, and if we require x = x' when t = 0, then the relation
between the space-time coordinates of the same event observed from the reference frames S' and
S, which are moving at a relative velocity of u in the x direction is:
x' = x − u·t
y' = y
z' = z
t' = t.
This set of formulas defines a group transformation known as the Galilean transformation
(informally, the Galilean transform). This group is a limiting case of the Poincaré group used in
special relativity. The limiting case applies when the velocity u is very small compared to c, the
speed of light.
The transformations have the following consequences:
v′ = v − u (the velocity v′ of a particle from the perspective of S′ is slower by u than its
velocity v from the perspective of S)
a′ = a (the acceleration of a particle is the same in any inertial reference frame)
F′ = F (the force on a particle is the same in any inertial reference frame)
the speed of light is not a constant in classical mechanics, nor does the special position
given to the speed of light in relativistic mechanics have a counterpart in classical
mechanics.
For some problems, it is convenient to use rotating coordinates (reference frames). Thereby one
can either keep a mapping to a convenient inertial frame, or introduce additionally a fictitious
centrifugal force and Coriolis force.

12. Forces; Newton's second law
Main articles: Force and Newton's laws of motion
Newton was the first to mathematically express the relationship between force and momentum.
Some physicists interpret Newton's second law of motion as a definition of force and mass, while
others consider it to be a fundamental postulate, a law of nature. Either interpretation has the
same mathematical consequences, historically known as "Newton's Second Law":
The quantity mv is called the (canonical) momentum. The net force on a particle is thus equal to
rate of change of momentum of the particle with time. Since the definition of acceleration is a =
dv/dt, the second law can be written in the simplified and more familiar form:
So long as the force acting on a particle is known, Newton's second law is sufficient to describe
the motion of a particle. Once independent relations for each force acting on a particle are
available, they can be substituted into Newton's second law to obtain an ordinary differential
equation, which is called the equation of motion.
As an example, assume that friction is the only force acting on the particle, and that it may be
modeled as a function of the velocity of the particle, for example:
where λ is a positive constant. Then the equation of motion is
This can be integrated to obtain
where v0 is the initial velocity. This means that the velocity of this particle decays exponentially
to zero as time progresses. In this case, an equivalent viewpoint is that the kinetic energy of the
particle is absorbed by friction (which converts it to heat energy in accordance with the
conservation of energy), slowing it down. This expression can be further integrated to obtain the
position r of the particle as a function of time.
Important forces include the gravitational force and the Lorentz force for electromagnetism. In
addition, Newton's third law can sometimes be used to deduce the forces acting on a particle: if it

13. is known that particle A exerts a force F on another particle B, it follows that B must exert an
equal and opposite reaction force, −F, on A. The strong form of Newton's third law requires that
F and −F act along the line connecting A and B, while the weak form does not. Illustrations of
the weak form of Newton's third law are often found for magnetic forces.
Work and energy
Main articles: Work (physics), kinetic energy, and potential energy
If a constant force F is applied to a particle that achieves a displacement Δr,[note 2] the work done
by the force is defined as the scalar product of the force and displacement vectors:
More generally, if the force varies as a function of position as the particle moves from r1 to r2
along a path C, the work done on the particle is given by the line integral
If the work done in moving the particle from r1 to r2 is the same no matter what path is taken, the
force is said to be conservative. Gravity is a conservative force, as is the force due to an idealized
spring, as given by Hooke's law. The force due to friction is non-conservative.
The kinetic energy Ek of a particle of mass m travelling at speed v is given by
For extended objects composed of many particles, the kinetic energy of the composite body is
the sum of the kinetic energies of the particles.
The work–energy theorem states that for a particle of constant mass m the total work W done on
the particle from position r1 to r2 is equal to the change in kinetic energy Ek of the particle:
Conservative forces can be expressed as the gradient of a scalar function, known as the potential
energy and denoted Ep:
If all the forces acting on a particle are conservative, and Ep is the total potential energy (which is
defined as a work of involved forces to rearrange mutual positions of bodies), obtained by
summing the potential energies corresponding to each force

14. This result is known as conservation of energy and states that the total energy,
is constant in time. It is often useful, because many commonly encountered forces are
conservative.
Beyond Newton's laws
Classical mechanics also includes descriptions of the complex motions of extended non-pointlike
objects. Euler's laws provide extensions to Newton's laws in this area. The concepts of angular
momentum rely on the same calculus used to describe one-dimensional motion. The rocket
equation extends the notion of rate of change of an object's momentum to include the effects of
an object "losing mass".
There are two important alternative formulations of classical mechanics: Lagrangian mechanics
and Hamiltonian mechanics. These, and other modern formulations, usually bypass the concept
of "force", instead referring to other physical quantities, such as energy, for describing
mechanical systems.
The expressions given above for momentum and kinetic energy are only valid when there is no
significant electromagnetic contribution. In electromagnetism, Newton's second law for current-
carrying wires breaks down unless one includes the electromagnetic field contribution to the
momentum of the system as expressed by the Poynting vector divided by c2, where c is the speed
of light in free space.
Limits of validity

15. Domain of validity for Classical Mechanics
Many branches of classical mechanics are simplifications or approximations of more accurate
forms; two of the most accurate being general relativity and relativistic statistical mechanics.
Geometric optics is an approximation to the quantum theory of light, and does not have a
superior "classical" form.
The Newtonian approximation to special relativity
In special relativity, the momentum of a particle is given by
where m is the particle's mass, v its velocity, and c is the speed of light.
If v is very small compared to c, v2/c2 is approximately zero, and so
Thus the Newtonian equation p = mv is an approximation of the relativistic equation for bodies
moving with low speeds compared to the speed of light.
For example, the relativistic cyclotron frequency of a cyclotron, gyrotron, or high voltage
magnetron is given by

16. where fc is the classical frequency of an electron (or other charged particle) with kinetic energy T
and (rest) mass m0 circling in a magnetic field. The (rest) mass of an electron is 511 keV. So the
frequency correction is 1% for a magnetic vacuum tube with a 5.11 kV direct current
accelerating voltage.
The classical approximation to quantum mechanics
The ray approximation of classical mechanics breaks down when the de Broglie wavelength is
not much smaller than other dimensions of the system. For non-relativistic particles, this
wavelength is
where h is Planck's constant and p is the momentum.
Again, this happens with electrons before it happens with heavier particles. For example, the
electrons used by Clinton Davisson and Lester Germer in 1927, accelerated by 54 volts, had a
wavelength of 0.167 nm, which was long enough to exhibit a single diffraction side lobe when
reflecting from the face of a nickel crystal with atomic spacing of 0.215 nm. With a larger
vacuum chamber, it would seem relatively easy to increase the angular resolution from around a
radian to a milliradian and see quantum diffraction from the periodic patterns of integrated
circuit computer memory.
More practical examples of the failure of classical mechanics on an engineering scale are
conduction by quantum tunneling in tunnel diodes and very narrow transistor gates in integrated
circuits.
Classical mechanics is the same extreme high frequency approximation as geometric optics. It is
more often accurate because it describes particles and bodies with rest mass. These have more
momentum and therefore shorter De Broglie wavelengths than massless particles, such as light,
with the same kinetic energies.
Branches

17. Branches of mechanics
Classical mechanics was traditionally divided into three main branches:
Statics, the study of equilibrium and its relation to forces
Dynamics, the study of motion and its relation to forces
Kinematics, dealing with the implications of observed motions without regard for
circumstances causing them
Another division is based on the choice of mathematical formalism:
Newtonian mechanics
Lagrangian mechanics
Hamiltonian mechanics
Alternatively, a division can be made by region of application:
Celestial mechanics, relating to stars, planets and other celestial bodies
Continuum mechanics, for materials which are modelled as a continuum, e.g., solids and
fluids (i.e., liquids and gases).
Relativistic mechanics (i.e. including the special and general theories of relativity), for
bodies whose speed is close to the speed of light.
Statistical mechanics, which provides a framework for relating the microscopic properties
of individual atoms and molecules to the macroscopic or bulk thermodynamic properties
of materials.
See also

18. Ten Different Types of Forces
By Erin Grady, eHow Contributor
The magnetic force that attracts
these paper clips is just one kind of force.
A force is an influence that causes physical change. There are ten basic kinds of forces: applied,
gravitational, normal, friction, air resistance, tension, spring, electrical, magnetic and upthrust.
Each of these forces does something different: some pull and some push, while others cause an
object to change form.
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1. Applied Force
o Applied force is transferred from a person or object to another person or object. If
a man is pushing his chair across a room, he is using applied force on the chair.
Gravitational Force

19. o Large objects have a gravitational force, which attracts smaller objects. The best
example of a gravitational force is the Earth's interaction with people, animals and
objects. Even the moon is pulled toward the Earth by a gravitational force.
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Normal Force
o Normal force is exerted on an object when it is in contact with another object.
When a coffee cup is resting on a table, the table is exerting a normal upward
force on the cup to support its weight.
Friction Force
o Friction occurs when an object moves -- or tries to move -- across a surface and
the surface opposes the object's movement. The amount of friction that is
generated depends on how strongly the two surfaces are being pushed together
and the nature of the surfaces. For example, pushing a book across a glassy
surface will not create much friction, while sliding your feet across carpet will
produce more friction.
Air Resistance Force
o Air resistance acts on objects as they travel through the air. This force will oppose
motion, but only factors in when objects travel at high speeds or have a large
surface area. For example, air resistance is smaller on a notebook falling from the
desk than a kite falling from a tree.
Tension Force
o Tension passes through strings, cables, ropes or wires when they are being pulled
in opposite directions. The tension force is directed along the length of the wire
and pulls equally on objects at opposite ends of the string, cable, rope or wire.
Spring Force
o Spring force is exerted when a compressed or stretched spring is trying to return
to an inert state. The string always wants to return to equilibrium and will do what
it can to do so.

20. Electrical Force
o Electrical force is an attraction between positively and negatively charged objects.
The closer the objects are to each other, the higher the electrical force.
Magnetic Force
o Magnetic force is an attraction force usually associated with electrical currents
and magnets. Magnetic force attracts opposite forces. Each magnet has a north
and a south end, each of which attracts the opposite ends of another magnet. For
example, a north magnetic end will attract a south magnetic end, and vice versa.
North ends of magnets repel each other, and vice versa. Magnets also create an
attractive force with certain metals.
Upthrust Force
o Upthrust is more commonly known as buoyancy. This is the upward thrust that is
caused by fluid pressure on objects, such as the pressure that allows boats to float.
Read more: Ten Different Types of Forces | eHow.com http://www.ehow.com/list_7459343_ten-
different-types-forces.html#ixzz2CfShdh8d
Average power
As a simple example, burning a kilogram of coal releases much more energy than does
detonating a kilogram of TNT,[3] but because the TNT reaction releases energy much more
quickly, it delivers far more power than the coal. If ΔW is the amount of work performed during
a period of time of duration Δt, the average power Pavg over that period is given by the formula
It is the average amount of work done or energy converted per unit of time. The average power is
often simply called "power" when the context makes it clear.
The instantaneous power is then the limiting value of the average power as the time interval Δt
approaches zero.

21. In the case of constant power P, the amount of work performed during a period of duration T is
given by:
In the context of energy conversion it is more customary to use the symbol E rather than W.
Mechanical power
Power in mechanical systems is the combination of forces and movement. In particular, power is
the product of a force on an object and the object's velocity, or the product of a torque on a shaft
and the shaft's angular velocity.
Mechanical power is also described as the time derivative of work. In mechanics, the work done
by a force F on an object that travels along a curve C is given by the line integral:
where x defines the path C and v is the velocity along this path. The time derivative of the
equation for work yields the instantaneous power,
In rotational systems, power is the product of the torque τ and angular velocity ω,
where ω measured in radians per second.
In fluid power systems such as hydraulic actuators, power is given by
where p is pressure in pascals, or N/m2 and Q is volumetric flow rate in m3/s in SI units.
Mechanical advantage
If a mechanical system has no losses then the input power must equal the output power. This
provides a simple formula for the mechanical advantage of the system.
Let the input power to a device be a force FA acting on a point that moves with velocity vA and
the output power be a force FB acts on a point that moves with velocity vB. If there are no losses
in the system, then

22. and the mechanical advantage of the system is given by
A similar relationship is obtained for rotating systems, where TA and ωA are the torque and
angular velocity of the input and TB and ωB are the torque and angular velocity of the output. If
there are no losses in the system, then
which yields the mechanical advantage
These relations are important because they define the maximum performance of a device in
terms of velocity ratios determined by its physical dimensions. See for example gear ratios.
Power in optics
In optics, or radiometry, the term power sometimes refers to radiant flux, the average rate of
energy transport by electromagnetic radiation, measured in watts. In other contexts, it refers to
optical power, the ability of a lens or other optical device to focus light. It is measured in dioptres
(inverse metres), and equals the inverse of the focal length of the optical device.
Electrical power
Main article: Electric power
The instantaneous electrical power P delivered to a component is given by
where
P(t) is the instantaneous power, measured in watts (joules per second)
V(t) is the potential difference (or voltage drop) across the component, measured in volts
I(t) is the current through it, measured in amperes
If the component is a resistor with time-invariant voltage to current ratio, then:

23. where
is the resistance, measured in ohms.
Peak power and duty cycle
In a train of identical pulses, the instantaneous power is a periodic function of time. The ratio of
the pulse duration to the period is equal to the ratio of the average power to the peak power. It is
also called the duty cycle (see text for definitions).
In the case of a periodic signal of period , like a train of identical pulses, the
instantaneous power is also a periodic function of period . The peak power is
simply defined by:
.
The peak power is not always readily measurable, however, and the measurement of the average
power is more commonly performed by an instrument. If one defines the energy per pulse
as:

24. then the average power is:
.
One may define the pulse length such that so that the ratios
are equal. These ratios are called the duty cycle of the pulse train.
A free body diagram, also called a force diagram,[1] is a pictorial representation
often used by physicists and engineers to analyze the forces acting on a body of
interest. A free body diagram shows all forces of all types acting on this body.
Drawing such a diagram can aid in solving for the unknown forces or the
equations of motion of the body. Creating a free body diagram can make it easier
to understand the forces, and torques or moments, in relation to one another and
suggest the proper concepts to apply in order to find the solution to a problem.
The diagrams are also used as a conceptual device to help identify the internal
forces—for example, shear forces and bending moments in beams—which are
developed within structures.[2][3] Number of sides
Polygons are primarily classified by the number of sides. See table below.
Convexity and types of non-convexity
Polygons may be characterized by their convexity or type of non-convexity:
Convex: any line drawn through the polygon (and not tangent to an edge or corner) meets
its boundary exactly twice. Equivalently, all its interior angles are less than 180°.
Non-convex: a line may be found which meets its boundary more than twice. In other
words, it contains at least one interior angle with a measure larger than 180°.
Simple: the boundary of the polygon does not cross itself. All convex polygons are
simple.
Concave: Non-convex and simple.
Star-shaped: the whole interior is visible from a single point, without crossing any edge.
The polygon must be simple, and may be convex or concave.
Self-intersecting: the boundary of the polygon crosses itself. Branko Grünbaum calls
these coptic, though this term does not seem to be widely used. The term complex is

25. sometimes used in contrast to simple, but this risks confusion with the idea of a complex
polygon as one which exists in the complex Hilbert plane consisting of two complex
dimensions.
Star polygon: a polygon which self-intersects in a regular way.
Symmetry
Equiangular: all its corner angles are equal.
Cyclic: all corners lie on a single circle.
Isogonal or vertex-transitive: all corners lie within the same symmetry orbit. The
polygon is also cyclic and equiangular.
Equilateral: all edges are of the same length. (A polygon with 5 or more sides can be
equilateral without being convex.) [1]
Isotoxal or edge-transitive: all sides lie within the same symmetry orbit. The polygon is
also equilateral.
Tangential: all sides are tangent to an inscribed circle.
Regular: A polygon is regular if it is both cyclic and equilateral. A non-convex regular
polygon is called a regular star polygon.
Miscellaneous
Rectilinear: a polygon whose sides meet at right angles, i.e., all its interior angles are 90
or 270 degrees.
Monotone with respect to a given line L, if every line orthogonal to L intersects the
polygon not more than twice.
Properties
Euclidean geometry is assumed throughout.
Angles
Any polygon, regular or irregular, self-intersecting or simple, has as many corners as it has sides.
Each corner has several angles. The two most important ones are:
Interior angle – The sum of the interior angles of a simple n-gon is (n − 2)π radians or (n
− 2)180 degrees. This is because any simple n-gon can be considered to be made up of (n
− 2) triangles, each of which has an angle sum of π radians or 180 degrees. The measure
of any interior angle of a convex regular n-gon is radians or
degrees. The interior angles of regular star polygons were first studied by Poinsot, in the
same paper in which he describes the four regular star polyhedra.
Exterior angle – Tracing around a convex n-gon, the angle "turned" at a corner is the
exterior or external angle. Tracing all the way around the polygon makes one full turn, so
the sum of the exterior angles must be 360°. This argument can be generalized to concave

26. simple polygons, if external angles that turn in the opposite direction are subtracted from
the total turned. Tracing around an n-gon in general, the sum of the exterior angles (the
total amount one rotates at the vertices) can be any integer multiple d of 360°, e.g. 720°
for a pentagram and 0° for an angular "eight", where d is the density or starriness of the
polygon. See also orbit (dynamics).
The exterior angle is the supplementary angle to the interior angle. From this the sum of the
interior angles can be easily confirmed, even if some interior angles are more than 180°: going
clockwise around, it means that one sometime turns left instead of right, which is counted as
turning a negative amount. (Thus we consider something like the winding number of the
orientation of the sides, where at every vertex the contribution is between −1⁄2 and 1⁄2 winding.)
Area and centroid
Nomenclature of a 2D polygon.
The area of a polygon is the measurement of the 2-dimensional region enclosed by the polygon.
For a non-self-intersecting (simple) polygon with n vertices, the area and centroid are given by:[2]
To close the polygon, the first and last vertices are the same, i.e., xn, yn = x0, y0. The vertices must
be ordered according to positive or negative orientation (counterclockwise or clockwise,
respectively); if they are ordered negatively, the value given by the area formula will be negative
but correct in absolute value. This is commonly called the Surveyor's Formula.[3]
The area formula is derived by taking each edge AB, and calculating the (signed) area of triangle
ABO with a vertex at the origin O, by taking the cross-product (which gives the area of a
parallelogram) and dividing by 2. As one wraps around the polygon, these triangles with positive
and negative area will overlap, and the areas between the origin and the polygon will be
cancelled out and sum to 0, while only the area inside the reference triangle remains. This is why
the formula is called the Surveyor's Formula, since the "surveyor" is at the origin; if going

27. counterclockwise, positive area is added when going from left to right and negative area is added
when going from right to left, from the perspective of the origin.
The formula was described by Meister[citation needed] in 1769 and by Gauss in 1795. It can be
verified by dividing the polygon into triangles, but it can also be seen as a special case of Green's
theorem.
The area A of a simple polygon can also be computed if the lengths of the sides, a1, a2, ..., an and
the exterior angles, θ1, θ2, ..., θn are known. The formula is
The formula was described by Lopshits in 1963.[4]
If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points,
Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior
and boundary grid points.
In every polygon with perimeter p and area A , the isoperimetric inequality holds.[5]
If any two simple polygons of equal area are given, then the first can be cut into polygonal pieces
which can be reassembled to form the second polygon. This is the Bolyai-Gerwien theorem.
The area of a regular polygon is also given in terms of the radius r of its inscribed circle and its
perimeter p by
.
This radius is also termed its apothem and is often represented as a.
The area of a regular n-gon with side s inscribed in a unit circle is
.
The area of a regular n-gon in terms of the radius r of its circumscribed circle and its perimeter p
is given by
.

28. The area of a regular n-gon, inscribed in a unit-radius circle, with side s and interior angle θ can
also be expressed trigonometrically as
.
The sides of a polygon do not in general determine the area.[6] However, if the polygon is cyclic
the sides do determine the area. Of all n-gons with given sides, the one with the largest area is
cyclic. Of all n-gons with a given perimeter, the one with the largest area is regular (and
therefore cyclic).[7]
Self-intersecting polygons
The area of a self-intersecting polygon can be defined in two different ways, each of which gives
a different answer:
Using the above methods for simple polygons, we discover that particular regions within
the polygon may have their area multiplied by a factor which we call the density of the
region. For example the central convex pentagon in the center of a pentagram has density
2. The two triangular regions of a cross-quadrilateral (like a figure 8) have opposite-
signed densities, and adding their areas together can give a total area of zero for the
whole figure.
Considering the enclosed regions as point sets, we can find the area of the enclosed point
set. This corresponds to the area of the plane covered by the polygon, or to the area of a
simple polygon having the same outline as the self-intersecting one (or, in the case of the
cross-quadrilateral, the two simple triangles).
Degrees of freedom
An n-gon has 2n degrees of freedom, including 2 for position, 1 for rotational orientation, and 1
for overall size, so 2n − 4 for shape. In the case of a line of symmetry the latter reduces to n − 2.
Let k ≥ 2. For an nk-gon with k-fold rotational symmetry (Ck), there are 2n − 2 degrees of
freedom for the shape. With additional mirror-image symmetry (Dk) there are n − 1 degrees of
freedom.
Product of distances from a vertex to other vertices of a regular polygon
For a regular n-gon inscribed in a unit-radius circle, the product of the distances from a given
vertex to all other vertices equals n.
Generalizations of polygons

29. In a broad sense, a polygon is an unbounded (without ends) sequence or circuit of alternating
segments (sides) and angles (corners). An ordinary polygon is unbounded because the sequence
closes back in itself in a loop or circuit, while an apeirogon (infinite polygon) is unbounded
because it goes on for ever so you can never reach any bounding end point. The modern
mathematical understanding is to describe such a structural sequence in terms of an "abstract"
polygon which is a partially ordered set (poset) of elements. The interior (body) of the polygon is
another element, and (for technical reasons) so is the null polytope or nullitope.
A geometric polygon is understood to be a "realization" of the associated abstract polygon; this
involves some "mapping" of elements from the abstract to the geometric. Such a polygon does
not have to lie in a plane, or have straight sides, or enclose an area, and individual elements can
overlap or even coincide. For example a spherical polygon is drawn on the surface of a sphere,
and its sides are arcs of great circles. So when we talk about "polygons" we must be careful to
explain what kind we are talking about.
A digon is a closed polygon having two sides and two corners. On the sphere, we can mark two
opposing points (like the North and South poles) and join them by half a great circle. Add
another arc of a different great circle and you have a digon. Tile the sphere with digons and you
have a polyhedron called a hosohedron. Take just one great circle instead, run it all the way
around, and add just one "corner" point, and you have a monogon or henagon – although many
authorities do not regard this as a proper polygon.
Other realizations of these polygons are possible on other surfaces, but in the Euclidean (flat)
plane, their bodies cannot be sensibly realized and we think of them as degenerate.
The idea of a polygon has been generalized in various ways. Here is a short list of some
degenerate cases (or special cases, depending on your point of view):
Digon: Interior angle of 0° in the Euclidean plane. See remarks above re. on the sphere.
Interior angle of 180°: In the plane this gives an apeirogon (see below), on the sphere a
dihedron
A skew polygon does not lie in a flat plane, but zigzags in three (or more) dimensions.
The Petrie polygons of the regular polyhedra are classic examples.
A spherical polygon is a circuit of sides and corners on the surface of a sphere.
An apeirogon is an infinite sequence of sides and angles, which is not closed but it has
no ends because it extends infinitely.
A complex polygon is a figure analogous to an ordinary polygon, which exists in the
complex Hilbert plane.
Naming polygons
The word "polygon" comes from Late Latin polygōnum (a noun), from Greek πολύγωνον
(polygōnon/polugōnon), noun use of neuter of πολύγωνος (polygōnos/polugōnos, the masculine
adjective), meaning "many-angled". Individual polygons are named (and sometimes classified)
according to the number of sides, combining a Greek-derived numerical prefix with the suffix -
gon, e.g. pentagon, dodecagon. The triangle, quadrilateral or quadrangle, and nonagon are

30. exceptions. For large numbers, mathematicians usually write the numeral itself, e.g. 17-gon. A
variable can even be used, usually n-gon. This is useful if the number of sides is used in a
formula.
Some special polygons also have their own names; for example the regular star pentagon is also
known as the pentagram.
Polygon names
Name Edges Remarks
henagon (or In the Euclidean plane, degenerates to a closed curve with a
1
monogon) single vertex point on it.
In the Euclidean plane, degenerates to a closed curve with two
digon 2
vertex points on it.
triangle (or trigon) 3 The simplest polygon which can exist in the Euclidean plane.
quadrilateral (or
quadrangle or 4 The simplest polygon which can cross itself.
tetragon)
The simplest polygon which can exist as a regular star. A star
pentagon 5
pentagon is known as a pentagram or pentacle.
hexagon 6 Avoid "sexagon" = Latin [sex-] + Greek.
Avoid "septagon" = Latin [sept-] + Greek. The simplest
polygon such that the regular form is not constructible with
heptagon 7
compass and straightedge. However, it can be constructed
using a Neusis construction.
octagon 8
"Nonagon" is commonly used but mixes Latin [novem = 9]
enneagon or nonagon 9 with Greek. Some modern authors prefer "enneagon", which is
pure Greek.
decagon 10
Avoid "undecagon" = Latin [un-] + Greek. The simplest
hendecagon 11 polygon such that the regular form cannot be constructed with
compass, straightedge, and angle trisector.
dodecagon 12 Avoid "duodecagon" = Latin [duo-] + Greek.
tridecagon (or
13
triskaidecagon)
tetradecagon (or
14
tetrakaidecagon)
pentadecagon (or
quindecagon or 15
pentakaidecagon)
hexadecagon (or
16
hexakaidecagon)

31. heptadecagon (or
17
heptakaidecagon)
octadecagon (or
18
octakaidecagon)
enneadecagon (or
enneakaidecagon or 19
nonadecagon)
icosagon 20
triacontagon 30
"hectogon" is the Greek name (see hectometer), "centagon" is a
hectogon 100
Latin-Greek hybrid; neither is widely attested.
René Descartes,[8] Immanuel Kant,[9] David Hume, [10] and
chiliagon 1000 others have used the chiliagon as an example in philosophical
discussion.
myriagon 10,000
As with René Descartes' example of the chiliagon, the million-
sided polygon has been used as an illustration of a well-defined
megagon[11][12][13] 1,000,000 concept that cannot be visualised.[14][15][16][17][18][19][20] The
megagon is also used as an illustration of the convergence of
regular polygons to a circle.[21]
apeirogon A degenerate polygon of infinitely many sides
Constructing higher names
To construct the name of a polygon with more than 20 and less than 100 edges, combine the
prefixes as follows
and Ones final suffix
Tens
1 -hena-
20 icosa- 2 -di-
30 triaconta- 3 -tri-
40 tetraconta- 4 -tetra-
50 pentaconta- -kai- 5 -penta- -gon
60 hexaconta- 6 -hexa-
70 heptaconta- 7 -hepta-
80 octaconta- 8 -octa-
90 enneaconta- 9 -ennea-
The "kai" is not always used. Opinions differ on exactly when it should, or need not, be used (see
also examples above).

32. Alternatively, the system used for naming the higher alkanes (completely saturated
hydrocarbons) can be used:
Ones Tens final suffix
1 hen- 10 deca-
2 do- 20 -cosa-
3 tri- 30 triaconta-
4 tetra- 40 tetraconta-
5 penta- 50 pentaconta- -gon
6 hexa- 60 hexaconta-
7 hepta- 70 heptaconta-
8 octa- 80 octaconta-
9 ennea- (or nona-) 90 enneaconta- (or nonaconta-)
This has the advantage of being consistent with the system used for 10- through 19-sided figures.
That is, a 42-sided figure would be named as follows:
Ones Tens final suffix full polygon name
do- tetraconta- -gon dotetracontagon
and a 50-sided figure
Tens and Ones final suffix full polygon name
pentaconta- -gon pentacontagon
But beyond enneagons and decagons, professional mathematicians generally prefer the
aforementioned numeral notation (for example, MathWorld has articles on 17-gons and 257-
gons). Exceptions exist for side counts that are more easily expressed in verbal form.
History
The component method is the concept that you can resolve vectors into two
independent (therefore perpendicular) vectors (say, in the x and y directions).
And, you can "put a vector back together" simply, using the distance formula
and the slope of the line.
So, the component form and the direction/magnitude forms are just two different
ways of specifying a vector. he Component Method for Vector Addition and
Scalar Multiplication

33. When we mentioned in the introduction that a vector is either an ordered pair or a triplet of
numbers we implicitly defined vectors in terms of components.
Each entry in the 2-dimensional ordered pair (a, b) or 3-dimensional triplet (a, b, c) is called a
component of the vector. Unless otherwise specified, it is normally understood that the entries
correspond to the number of units the vector has in the x , y , and (for the 3D case) z directions of
a plane or space. In other words, you can think of the components as simply the coordinates of
the point associated with the vector. (In some sense, the vector is the point, although when we
draw vectors we normally draw an arrow from the origin to the point.)
Figure %: The vector (a, b) in the Euclidean plane.
Vector Addition Using Components
Given two vectors u = (u 1, u 2) and v = (v 1, v 2) in the Euclidean plane, the sum is given by:
u + v = (u 1 + v 1, u 2 + v 2)
For three-dimensional vectors u = (u 1, u 2, u 3) and v = (v 1, v 2, v 3) , the formula is almost
identical:
u + v = (u 1 + v 1, u 2 + v 2, u 3 + v 3)
In other words, vector addition is just like ordinary addition: component by component.
Notice that if you add together two 2-dimensional vectors you must get another 2-dimensional
vector as your answer. Addition of 3-dimensional vectors will yield 3-dimensional answers. 2-
and 3-dimensional vectors belong to different vector spaces and cannot be added. These same
rules apply when we are dealing with scalar multiplication.
Scalar Multiplication of Vectors Using Components

34. Given a single vector v = (v 1, v 2) in the Euclidean plane, and a scalar a (which is a real number),
the multiplication of the vector by the scalar is defined as:
av = (av 1, av 2)
Similarly, for a 3-dimensional vector v = (v 1, v 2, v 3) and a scalar a , the formula for scalar
multiplication is:
av = (av 1, av 2, av 3)
So what we are doing when we multiply a vector by a scalar a is obtaining a new vector (of the
same dimension) by multiplying each component of the original vector by a .
Unit Vectors
For 3-dimensional vectors, it is often customary to define unit vectors pointing in the x , y , and z
directions. These vectors are usually denoted by the letters i , j , and k , respectively, and all have
length 1 . Thus, i = (1, 0, 0) , j = (0, 1, 0) , and k = (0, 0, 1) . This enables us to write a vector as
a sum in the following way:
(a, b, c) = a(1, 0, 0) + b(0, 1, 0) + c(0, 0, 1)
=a i + b j + c k
Vector Subtraction
Subtraction for vectors (as with ordinary numbers) is not a new operation. If you want to perform
the vector subtraction u - v , you simply use the rules for vector addition and scalar
multiplication: u - v = u + (- 1)v .
In the next section, we will see how these rules for addition and scalar multiplication of vectors
can be understood in a geometric way. We will find, for instance, that vector addition can be
done graphically (i.e. without even knowing the components of the vectors involved), and that
scalar multiplication of a vector amounts to a change in the vector's magnitude, but does not alter
its direction.
Resultant force refers to the reduction of a system of forces acting on a body to a single force
and an associated torque. The choice of the point of application of the force determines the

35. associated torque.[1] The term resultant force should be understood to refer to both the forces and
torques acting on a rigid body, which is why some use the term resultant force-torque.
The resultant force, or resultant force-torque, fully replaces the effects of all forces on the motion
of the rigid body they act upon.
Associated torque
If a point R is selected as the point of application of the resultant force F of a system of n forces
Fi then the associated torque T is determined from the formulas
and
It is useful to note that the point of application R of the resultant force may be anywhere along
the line of action of F without changing the value of the associated torque. To see this add the
vector kF to the point of application R in the calculation of the associated torque,
The right side of this equation can be separated into the original formula for T plus the additional
term including kF,
Now because F is the sum of the vectors Fi this additional term is zero, that is
and the value of the associated torque is unchanged.
Torque-free resultant

36. it is useful to consider whether there is a point of application R such that the associated torque is
zero. This point is defined by property
where F is resultant force and Fi form the system of forces.
Notice that this equation for R has a solution only if the sum of the individual torques on the
right side yield a vector that is perpendicular to F. Thus, the condition that a system of forces has
a torque-free resultant can be written as
If this condition is not satisfied, then the system of forces includes a pure torque.
The diagram illustrates simple graphical methods for finding the line of application of the
resultant force of simple planar systems.
1. Lines of application of the actual forces and on the leftmost illustration intersect.
After vector addition is performed "at the location of ", the net force obtained is
translated so that its line of application passes through the common intersection point.
With respect to that point all torques are zero, so the torque of the resultant force is
equal to the sum of the torques of the actual forces.
2. Illustration in the middle of the diagram shows two parallel actual forces. After vector
addition "at the location of ", the net force is translated to the appropriate line of
application, where it becomes the resultant force . The procedure is based on
decomposition of all forces into components for which the lines of application (pale
dotted lines) intersect at one point (the so called pole, arbitrarily set at the right side of the
illustration). Then the arguments from the previous case are applied to the forces and
their components to demonstrate the torque relationships.
3. The rightmost illustration shows a couple, two equal but opposite forces for which the
amount of the net force is zero, but they produce the net torque where is the
distance between their lines of application. This is "pure" torque, since there is no
resultant force.
Wrench
The forces and torques acting on a rigid body can be assembled into the pair of vectors called a
wrench.[2] Let P be the point of application of the force F and let R be the vector locating this
point in a fixed frame. Then the pair of vectors W=(F, R×F) is called a wrench. Vectors of this
form are know as screws and their mathematics formulation is called screw theory.[3][4]

37. The resultant force and torque on a rigid body obtained from a system of forces Fi i=1,...,n, is
simply the sum of the individual wrenches Wi, that is
Notice that the case of two equal but opposite forces F and -F acting at points A and B
respectively, yields the resultant W=(F-F, A×F - B× F) = (0, (A-B)×F). This shows that
wrenches of the form W=(0, T) can be interpreted as pure torques.
What are the Main Branches of Natural Science
Natural science involves the study of phenomena or laws of physical world. Following are the
key branches of natural science. Read on...
Natural science can be defined as a rational approach to the study of the universe and the
physical world. Astronomy, biology, chemistry, earth science and physics are the main branches
of natural science. There are some cross-disciplines of natural science such as astrophysics,
biophysics, physical chemistry, geochemistry, biochemistry, astrochemistry, etc.
Astronomy deals with the scientific study of celestial bodies including stars, comets, planets and
galaxies and phenomena that originate outside the earth's atmosphere such as the cosmic
background radiation.
Biology or biological science is the scientific study of living things, including the study of their
structure, origin, growth, evolution, function and distribution. Different branches of biology are
zoology, botany, genetics, ecology, marine biology and biochemistry.
Chemistry is a branch of natural science that deals with the composition of substances as well as
their properties and reactions. It involves the study of matter and its interactions with energy and
itself. Today, a number of disciplines exist under the various branches of chemistry.
Earth science includes the study of the earth's system in space that includes weather and climate
systems as well as the study of nonliving things such as oceans, rocks and planets. It deals with
the physical aspects of the earth, such as its formation, structure, and related phenomena. It
includes different branches such as geology, geography, meteorology, oceanography and
astronomy.
Physics is a branch of natural science that is associated with the study of properties and
interactions of time, space, energy and matter.
Read more at Buzzle: http://www.buzzle.com/articles/what-are-the-main-branches-of-natural-
science.html
In physics, a scalar is a simple physical quantity that is unchanged by coordinate system
rotations or translations (in Newtonian mechanics), or by Lorentz transformations or central-time
translations (in relativity). A scalar is a quantity which can be described by a single number,
unlike vectors, tensors, etc. which are described by several numbers which describe magnitude

38. and direction. A related concept is a pseudoscalar, which is invariant under proper rotations but
(like a pseudovector) flips sign under improper rotations. The concept of a scalar in physics is
essentially the same as in mathematics.
An example of a scalar quantity is temperature; the temperature at a given point is a single
number. Velocity, for example, is a vector quantity. Velocity in four-dimensional space is
specified by three values; in a Cartesian coordinate system the values are the speeds relative to
each coordinate axis.
Vector, a Latin word meaning "carrier",In mathematics,
Direction is the information contained in the relative position of one point with respect to another point
without the distance information. Directions may be either relative to some indicated reference (the
violins in a full orchestra are typically seated to the left of the conductor), or absolute according to some
previously agreed upon frame of reference (New York City lies due west of Madrid). Direction is often
indicated manually by an extended index finger or written as an arrow. On a vertically oriented sign
representing a horizontal plane, such as a road sign, "forward" is usually indicated by an upward arrow.
Mathematically, direction may be uniquely specified by a unit vector, or equivalently by the angles made
by the most direct path with respect to a specified set of axes.
magnitude is the "size" of a mathematical object, a property by which the object can be compared as
larger or smaller than other objects of the same kind. More formally, an object's magnitude is an
ordering (or ranking) of the class of objects to which it belongs.
When referring to a two and three-dimensional plane, the x-axis or horizontal axis refers to the
horizontal width of a two or three-dimensional object. In the picture to the right, the x-axis plane goes
left-to-right and intersects with the y-axis and z-axis. A good example of where the x-axis is used on a
computer is with the mouse. By assigning a value to the x-axis, when the mouse is moved left-to-right
the x-axis value increases and decreases, which allows the computer to know where the mouse cursor is
on the screen.
he vertical axis of a two-dimensional plot in Cartesian coordinates. Physicists and astronomers
sometimes call this axis the ordinate, although that term is more commonly used to refer to
coordinates along the -axis. n physics, a force is any influence that causes an object to undergo
a certain change, either concerning its movement, direction, or geometrical construction. It is
measured with the SI unit of newtons and represented by the symbol F. In other words, a force is
that which can cause an object with mass to change its velocity (which includes to begin moving
from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform. Force can
also be described by intuitive concepts such as a push or pull. A force has both magnitude and
direction, making it a vector quantity.
The original form of Newton's second law states that the net force acting upon an object is equal
to the rate at which its momentum changes.[1] This law is further given to mean that the
acceleration of an object is directly proportional to the net force acting on the object, is in the

39. direction of the net force, and is inversely proportional the mass of the object. As a formula, this
is expressed as:
where the arrows imply a vector quantity possessing both magnitude and direction.
Related concepts to force include: thrust, which increases the velocity of an object; drag, which
decreases the velocity of an object; and torque which produces changes in rotational speed of an
object. Forces which do not act uniformly on all parts of a body will also cause mechanical
stresses,[2] a technical term for influences which cause deformation of matter. While mechanical
stress can remain embedded in a solid object, gradually deforming it, mechanical stress in a fluid
determines changes in its pressure and volume.[3][4]