science concerned with the motion of bodies under the action of
forces, including the special case in which a body remains at rest

a self-propagating wave in space with electric and magnetic
components. These components oscillate at right angles to each other
and to the direction of propagation, and are in phase with each other.
Electromagnetic radiation is classified into types according to the
frequency of the wave: these types include, in order of increasing
frequency, radio waves, microwaves, terahertz radiation, infrared
radiation, visible light, ultraviolet radiation, X-rays and gamma rays.

branch of physics that studies the elementary constituents of matter
and radiation, and the interactions between them. It is also
called "high energy physics", because many elementary particles do not
occur under normal circumstances in nature, but can be created and
detected during energetic collisions of other particles, as is done in
particle accelerators.

the field of physics that deals with the macroscopic physical
properties of matter. In particular, it is concerned with
the "condensed" phases that appear whenever the number of constituents
in a system is extremely large and the interactions between the
constituents are strong. The most familiar examples of condensed
phases are solids and liquids, which arise from the bonding and
electromagnetic force between atoms. More exotic condensed phases
include the superfluid and the Bose-Einstein condensate found in
certain atomic systems at very low temperatures, the superconducting
phase exhibited by conduction electrons in certain materials, and the
ferromagnetic and antiferromagnetic phases of spins on atomic lattices.

the study of statistical ensembles of quantum mechanical systems. A
statistical ensemble is described by a density operator S, which is a
non-negative, self-adjoint, trace-class operator of trace 1 on the
Hilbert space H describing the quantum system. This can be shown under
various mathematical formalisms for quantum mechanics. One such
formalism is provided by quantum logic.

the research and analysis of the mechanics of living organisms. As
such it is a branch of both mechanics and biology.

Among the subjects that biomechanics investigates are the forces that
act on limbs, the aerodynamics of bird and insect flight, the
hydrodynamics of swimming in fish and locomotion in general across all
forms of life, from individual cells to whole organisms. The
biomechanics of human beings is a core part of kinesiology.

deals with the study of the solutions to the equations of motion of
systems that are primarily mechanical in nature; although this
includes both planetary orbits as well as the behaviour of electronic
circuits and the solutions to partial differential equations that
arise in biology. Much of modern research is focused on the study of
chaotic systems

In physics, magnetism is one of the phenomena by which materials exert
attractive or repulsive forces on other materials. Some well known
materials that exhibit easily detectable magnetic properties (called
magnets) are nickel, iron and their alloys; however, all materials are
influenced to greater or lesser degree by the presence of a magnetic
field.

Scalar
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A scalar is a variable that only has magnitude, e.g. a speed of 40
km/h. Compare it with vector, a quantity comprising both magnitude and
direction, e.g. a velocity of 40km/h north.

Look up scalar in Wiktionary, the free dictionary.A scalar
(mathematics), a quantity which is independent of viewpoint, a non-
tensor.
A scalar (physics), the same as the notion of scalar in differential
geometry.
A scalar (computing), an atomic quantity that can hold only one value
at a time.

In mathematics and physics, a scalar field associates a scalar value,
which can be either mathematical in definition, or physical, to every
point in space. Scalar fields are often used in physics, for instance
to indicate the temperature distribution throughout space, or the air
pressure. In mathematics, or more specifically, differential geometry,
the set of functions defined on a manifold define the commutative ring
of functions.

Just as the concept of a scalar in mathematics is identical to the
concept of a scalar in physics, so also the scalar field defined in
differential geometry is identical to, in the abstract, to the
(unquantized) scalar fields of physics.

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In mathematics, scalar multiplication is one of the basic operations
defining a vector space in linear algebra (or more generally, a
module in abstract algebra). Note that scalar multiplication is
different from scalar product which is an inner product between two
vectors.

More specifically, if K is a field and V is a vector space over K,
then scalar multiplication is a function from K × V to V. The result
of applying this function to c in K and v in V is cv.

Scalar multiplication obeys the following rules (vector in boldface):

Left distributivity: (c + d)v = cv + dv;
Right distributivity: c(v + w) = cv + cw;
Associativity: (cd)v = c(dv);
Multiplying by 1 does not change a vector: 1v = v;
Multiplying by 0 gives the null vector: 0v = 0;
Multiplying by -1 gives the additive inverse: (-1)v = -v.
Here + is addition either in the field or in the vector space, as
appropriate; and 0 is the additive identity in either. Juxtaposition
indicates either scalar multiplication or the multiplication
operation in the field.

Scalar multiplication may be viewed as an external binary operation
or as an action of the field on the vector space. A geometric
interpretation to scalar multiplication is a stretching or shrinking
of a vector.

As a special case, V may be taken to be K itself and scalar
multiplication may then be taken to be simply the multiplication in
the field. When V is Kn, then scalar multiplication is defined
component-wise.

The same idea goes through with no change if K is a commutative ring
and V is a module over K. K can even be a rig, but then there is no
additive inverse. If K is not commutative, then the only change is
that the order of the multiplication may be reversed from what we've
written above

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For the scalar product or dot product of spatial vectors, see dot
product.

Geometric interpretation of inner productIn mathematics, an inner
product space is a vector space of arbitrary (possibly infinite)
dimension with additional structure, which, among other things,
enables generalization of concepts from two or three-dimensional
Euclidean geometry. The additional structure associates to each pair
of vectors in the space a number which is called the inner product
(also called a scalar product) of the vectors. Inner products allow
the rigorous introduction of intuitive geometrical notions such as
the angle between vectors or length of vectors in spaces of all
dimensions. It also allows introduction of the concept of
orthogonality between vectors. Inner product spaces generalize
Euclidean spaces (with the dot product as the inner product) and are
studied in functional analysis.

An inner product space is sometimes also called a pre-Hilbert space,
since its completion with respect to the metric induced by its inner
product is a Hilbert space.

Inner product spaces were referred to as unitary spaces in earlier
work, although this terminology is now rarely used.

•
In physics, a pseudoscalar is a quantity that behaves like a scalar,
except that it changes sign under a parity inversion such as improper
rotations while true scalar does not.

The prototypical example of a pseudoscalar is the scalar triple
product. A pseudoscalar, when multiplied by an ordinary vector,
becomes a pseudovector or axial vector; a similar construction creates
the pseudotensor.

Mathematically, a pseudoscalar is an element of the top exterior power
of a vector space. More generally, it is an element of the canonical
bundle of a differentiable manifold.

Kinematics (Greek êéíåéí,kinein, to move) is a branch of mechanics
which describes the motion of objects without the consideration of the
masses or forces that bring about the motion. In contrast, dynamics is
concerned with the forces and interactions that produce or affect the
motion.

Vector Properties

It is the convention to print vectors in boldface type to distinguish
them from scalars. Graphically speaking, an arrow can conveniently and
effectively represent a vector. The length of the arrow is
proportional to its magnitude while the tip of the arrow shows its
direction

The simplest application of kinematics is to point particle motion
(translational kinematics or linear kinematics). The description of
rotation (rotational kinematics or angular kinematics) is more
complicated. The state of a generic rigid body may be described by
combining both translational and rotational kinematics (rigid-body
kinematics). A more complicated case is the kinematics of a system of
rigid bodies, possibly linked together by mechanical joints. The
kinematic description of fluid flow is even more complicated, and not
generally thought of in the context of kinematics.

Two dimensional rotating reference frame
This coordinate system only expresses planar motion.

This system of coordinates is based on three orthogonal unit vectors:
the vector i, and the vector j which form a basis for the plane in
which the objects we are considering reside, and k about which
rotation occurs. Unlike rectangular coordinates, which are measured
relative to an origin that is fixed and non rotating, the origin of
these coordinates can rotate and translate - often following a
particle on a body that is being studied.

Position, velocity, and acceleration
Given these identities, we can now figure out how to represent the
position, velocity, and acceleration vectors of a particle using this
reference frame.

Inextensible cord
This is the case where bodies are connected by some cord that remains
in tension and cannot change length. The constraint is that the sum of
all components of the cord, however they are defined, is the total
length, and the time derivative of this sum is zero.

In physics, motion means a continuous change in the position of a body
relative to a reference point, as measured by a particular observer in
a particular frame of reference. Until the end of the 19th century,
Isaac Newton's laws of motion, which he posited as axioms or
postulates in his famous Principia were the basis of what has since
become known as classical physics. Calculations of trajectories and
forces of bodies in motion based on Newtonian or classical physics
were very successful until physicists began to be able to measure and
observe very fast physical phenomena.

In physics, equations of motion are equations that describe the
behavior of a system (e.g., the motion of a particle under an
influence of a force) as a function of time. Sometimes the term refers
to the differential equations that the system satisfies (e.g.,
Newton's second law or Euler-Lagrange equations), and sometimes to the
solutions to those equations.

The equations that apply to bodies moving linearly (that is, one
dimension) with uniform acceleration are presented below. They are
often referred to as SUVAT equations, as the 5 variables they involve
are represented by those letters (S = displacement, U = initial
velocity, V = final velocity, A = acceleration, T = time)

Newton's laws of motion are three physical laws which provide
relationships between the forces acting on a body and the motion of
the body. They were first compiled by Sir Isaac Newton in his work
Philosophiae Naturalis Principia Mathematica (1687). The laws form the
basis for classical mechanics and Newton himself used them to explain
many results concerning the motion of physical objects. In the third
volume of the text, he showed that these laws of motion, combined with
his law of universal gravitation, explained Kepler's laws of planetary
motion.

In physics, the ballistic trajectory of a projectile is the path that
a thrown object will take under the action of gravity, neglecting all
other forces, such as friction from air resistance, or propulsion.
This article provides a list of methods for calculating the trajectory
of a projectile under the influence of Earth's gravity.

In physics, a rigid body is an idealization of a solid body of finite
size in which deformation is neglected. In other words, the distance
between any two given points of a rigid body remains constant in time
regardless of external forces exerted on it. In classical mechanics a
rigid body is usually considered as a continuous mass distribution,
while in quantum mechanics a rigid body is usually thought of as a
collection of point masses. For instance, in quantum mechanics
molecules (consisting of the point masses: electrons and nuclei) are
often seen as rigid bodies (see classification of molecules as rigid
rotors).

is the branch of physics concerned with the behaviour of physical
bodies when subjected to forces or displacements, and the subsequent
effect of the bodies on their environment.

The discipline has its roots in several ancient civilizations: ancient
Greece, where Aristotle studied the way bodies behaved when they were
thrown through the air (e.g. a stone); ancient China, with figures such
as Zhang Heng, Shen Kuo, and Su Song; and ancient India, with thinkers
such as Kanada, Aryabhata, and Brahmagupta. During the Middle Ages,
significant contributions to mechanics were made by Muslim scientists,
such as Muhammad ibn Musa, Alhacen, Avicenna, Avempace, al-Baghdadi,
and al-Khazini. During the early modern period, scientists such as
Galileo, Kepler, and especially Newton, laid the foundation for what is
now known as Newtonian mechanics.

A person working in the discipline is known as a mechanician.

Classical thermodynamics is the original early 1800s variation of
thermodynamics concerned with thermodynamic states, and properties as
energy, work, and heat, and with the laws of thermodynamics, all
lacking an atomic interpretation. In precursory form, classical
thermodynamics derives from chemist Robert Boyle's 1662 postulate that
the pressure P of a given quantity of gas varies inversely as its
volume V at constant temperature; i.e. in equation form: PV = k, a
constant. From here, a semblance of a thermo-science began to develop
with the construction of the first successful atmospheric steam
engines in England by Thomas Savery in 1697 and Thomas Newcomen in
1712. The first and second laws of thermodynamics emerged
simultaneously in the 1850s, primarily out of the works of William
Rankine, Rudolf Clausius, and William Thomson (Lord Kelvin).

displacement is the vector that specifies the position of a point or
a particle in reference to an origin or to a previous position. The
vector directs from the reference point to the current position.


Displacement vector versus distance traveled along a pathWhen the
reference point is the origin of the chosen coordinate system, the
displacement vector is better referred to as the position vector,
which expresses position by the straight line directed from the
previous position to the current position, as opposed to the scalar
quantity distance which expresses only the length. This use of
displacement vector can describe the complete motion as well as the
path of the particle.

When the reference point is a previous position of the particle, the
displacement vector indicates the sense of movement by a vector
directing from the previous position to the current position. This
use of displacement vector is useful for defining the velocity and
acceleration vectors of the particle.

By plotting the displacement, relative to the starting point, against
time on a position vs. time graph, the average velocity or the
instantaneous velocity can be found by taking the slope of the graph
or the derivative of the graph, respectively.

In dealing with the motion of a rigid/firm body, the term
displacement may also include the rotations of the body.

With the development of atomic and molecular theories in the late 19th
century, thermodynamics was given a molecular interpretation. This
field is called statistical thermodynamics, which can be thought of as
a bridge between macroscopic and microscopic properties of systems.
[11] Essentially, statistical thermodynamics is an approach to
thermodynamics situated upon statistical mechanics, which focuses on
the derivation of macroscopic results from first principles. It can be
opposed to its historical predecessor phenomenological thermodynamics,
which gives scientific descriptions of phenomena with avoidance of
microscopic details. The statistical approach is to derive all
macroscopic properties (temperature, volume, pressure, energy,
entropy, etc.) from the properties of moving constituent particles and
the interactions between them (including quantum phenomena). It was
found to be very successful and thus is commonly used.

Chemical thermodynamics is the study of the interrelation of heat with
chemical reactions or with a physical change of state within the
confines of the laws of thermodynamics. During the years 1873-76 the
American mathematical physicist Josiah Willard Gibbs published a
series of three papers, the most famous being On the Equilibrium of
Heterogeneous Substances, in which he showed how thermodynamic
processes could be graphically analyzed, by studying the energy,
entropy, volume, temperature and pressure of the thermodynamic system,
in such a manner to determine if a process would occur spontaneously.
[12] During the early 20th century, chemists such as Gilbert N. Lewis,
Merle Randall, and E. A. Guggenheim began to apply the mathematical
methods of Gibbs to the analysis of chemical processes.[13]

A spatial vector, or simply vector, is a concept characterized by a
magnitude and a direction. A vector can be thought of as an arrow in
Euclidean space, drawn from an initial point A pointing to a terminal
point B. This vector is commonly denoted by


indicating that the arrow points from A to B. In this way, the arrow
holds all the information of the vector quantity — the magnitude is
represented by the arrow's length and the direction by the direction
of the arrow's head and body. This magnitude and direction are those
necessary to carry one from A to B. [1]

Vectors have a variety of algebraic properties. Vectors may be scaled
by stretching them out, or compressing them. They can be flipped
around so as to point in the opposite direction. Two vectors sharing
the same initial point can also be added or subtracted.