Coordinate system

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Coordinate_system

The spherical coordinate system is commonly used in physics. It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance r, polar angle θ (theta), and azimuthal angle φ (phi). The symbol ρ (rho) is often used instead of r.

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

Common coordinate systems

Number line

Main article: Number line

The simplest example of a coordinate system is the identification of points on a line with real numbers using the number line. In this system, an arbitrary point O (the origin) is chosen on a given line. The coordinate of a point P is defined as the signed distance from O to P, where the signed distance is the distance taken as positive or negative depending on which side of the line P lies. Each point is given a unique coordinate and each real number is the coordinate of a unique point.

Cartesian coordinate system

Main article: Cartesian coordinate system

 

The Cartesian coordinate system in the plane

 

The Cartesian coordinate system in three-dimensional space

The prototypical example of a coordinate system is the Cartesian coordinate system. In the plane, two perpendicular lines are chosen and the coordinates of a point are taken to be the signed distances to the lines. In three dimensions, three mutually orthogonal planes are chosen and the three coordinates of a point are the signed distances to each of the planes. This can be generalized to create n coordinates for any point in n-dimensional Euclidean space.

Depending on the direction and order of the coordinate axes, the three-dimensional system may be a right-handed or a left-handed system.

Polar coordinate system

Main article: Polar coordinate system

Another common coordinate system for the plane is the polar coordinate system. A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line). Then there is a unique point on this line whose signed distance from the origin is r for given number r. For a given pair of coordinates (r, θ) there is a single point, but any point is represented by many pairs of coordinates. For example, (r, θ), (r, θ+2π) and (−r, θ+π) are all polar coordinates for the same point. The pole is represented by (0, θ) for any value of θ.

Cylindrical and spherical coordinate systems

Main articles: Cylindrical coordinate system and Spherical coordinate system

Cylindrical coordinate system

There are two common methods for extending the polar coordinate system to three dimensions. In the cylindrical coordinate system, a z-coordinate with the same meaning as in Cartesian coordinates is added to the r and θ polar coordinates giving a triple (r, θ, z). Spherical coordinates take this a step further by converting the pair of cylindrical coordinates (r, z) to polar coordinates (ρ, φ) giving a triple (ρ, θ, φ).

Homogeneous coordinate system

Main article: Homogeneous coordinates

A point in the plane may be represented in homogeneous coordinates by a triple (x, y, z) where x/z and y/z are the Cartesian coordinates of the point. This introduces an "extra" coordinate since only two are needed to specify a point on the plane, but this system is useful in that it represents any point on the projective plane without the use of infinity. In general, a homogeneous coordinate system is one where only the ratios of the coordinates are significant and not the actual values.

Other commonly used systems

Some other common coordinate systems are the following:

• Curvilinear coordinates are a generalization of coordinate systems generally; the system is based on the intersection of curves.
  • Orthogonal coordinates: coordinate surfaces meet at right angles
  • Skew coordinates: coordinate surfaces are not orthogonal
• The log-polar coordinate system represents a point in the plane by the logarithm of the distance from the origin and an angle measured from a reference line intersecting the origin.
• Plücker coordinates are a way of representing lines in 3D Euclidean space using a six-tuple of numbers as homogeneous coordinates.
• Generalized coordinates are used in the Lagrangian treatment of mechanics.
• Canonical coordinates are used in the Hamiltonian treatment of mechanics.
• Barycentric coordinate system as used for ternary plots and more generally in the analysis of triangles.
• Trilinear coordinates are used in the context of triangles.

There are ways of describing curves without coordinates, using intrinsic equations that use invariant quantities such as curvature and arc length. These include:

• The Whewell equation relates arc length and the tangential angle.
• The Cesàro equation relates arc length and curvature.

Coordinates of geometric objects

Coordinates systems are often used to specify the position of a point, but they may also be used to specify the position of more complex figures such as lines, planes, circles or spheres. For example, Plücker coordinates are used to determine the position of a line in space. When there is a need, the type of figure being described is used to distinguish the type of coordinate system, for example the term line coordinates is used for any coordinate system that specifies the position of a line.

It may occur that systems of coordinates for two different sets of geometric figures are equivalent in terms of their analysis. An example of this is the systems of homogeneous coordinates for points and lines in the projective plane. The two systems in a case like this are said to be dualistic. Dualistic systems have the property that results from one system can be carried over to the other since these results are only different interpretations of the same analytical result; this is known as the principle of duality.

Transformations

For broader coverage of this topic, see Geometric transformation.

For a more comprehensive list, see List of common coordinate transformations.

See also: Active and passive transformation

There are often many different possible coordinate systems for describing geometrical figures. The relationship between different systems is described by coordinate transformations, which give formulas for the coordinates in one system in terms of the coordinates in another system. For example, in the plane, if Cartesian coordinates (x, y) and polar coordinates (r, θ) have the same origin, and the polar axis is the positive x axis, then the coordinate transformation from polar to Cartesian coordinates is given by x = r cosθ and y = r sinθ.

With every bijection from the space to itself two coordinate transformations can be associated:

• Such that the new coordinates of the image of each point are the same as the old coordinates of the original point (the formulas for the mapping are the inverse of those for the coordinate transformation)
• Such that the old coordinates of the image of each point are the same as the new coordinates of the original point (the formulas for the mapping are the same as those for the coordinate transformation)

For example, in 1D, if the mapping is a translation of 3 to the right, the first moves the origin from 0 to 3, so that the coordinate of each point becomes 3 less, while the second moves the origin from 0 to −3, so that the coordinate of each point becomes 3 more.

Coordinate lines/curves

"Coordinate line" redirects here. Not to be confused with Line coordinates.

Given a coordinate system, if one of the coordinates of a point varies while the other coordinates are held constant, then the resulting curve is called a coordinate curve. If a coordinate curve is a straight line, it is called a coordinate line. A coordinate system for which some coordinate curves are not lines is called a curvilinear coordinate system. Orthogonal coordinates are a special but extremely common case of curvilinear coordinates.

A coordinate line with all other constant coordinates equal to zero is called a coordinate axis, an oriented line used for assigning coordinates. In a Cartesian coordinate system, all coordinates curves are lines, and, therefore, there are as many coordinate axes as coordinates. Moreover, the coordinate axes are pairwise orthogonal.

A polar coordinate system is a curvilinear system where coordinate curves are lines or circles. However, one of the coordinate curves is reduced to a single point, the origin, which is often viewed as a circle of radius zero. Similarly, spherical and cylindrical coordinate systems have coordinate curves that are lines, circles or circles of radius zero.

Many curves can occur as coordinate curves. For example, the coordinate curves of parabolic coordinates are parabolas.

Coordinate planes/surfaces

"Coordinate plane" redirects here. Not to be confused with Plane coordinates.

Coordinate surfaces of the three-dimensional paraboloidal coordinates.

In three-dimensional space, if one coordinate is held constant and the other two are allowed to vary, then the resulting surface is called a coordinate surface. For example, the coordinate surfaces obtained by holding ρ constant in the spherical coordinate system are the spheres with center at the origin. In three-dimensional space the intersection of two coordinate surfaces is a coordinate curve. In the Cartesian coordinate system we may speak of coordinate planes. Similarly, coordinate hypersurfaces are the (n − 1)-dimensional spaces resulting from fixing a single coordinate of an n-dimensional coordinate system.

Coordinate maps

Main article: Coordinate map

Further information: Manifold

The concept of a coordinate map, or coordinate chart is central to the theory of manifolds. A coordinate map is essentially a coordinate system for a subset of a given space with the property that each point has exactly one set of coordinates. More precisely, a coordinate map is a homeomorphism from an open subset of a space X to an open subset of Rⁿ. It is often not possible to provide one consistent coordinate system for an entire space. In this case, a collection of coordinate maps are put together to form an atlas covering the space. A space equipped with such an atlas is called a manifold and additional structure can be defined on a manifold if the structure is consistent where the coordinate maps overlap. For example, a differentiable manifold is a manifold where the change of coordinates from one coordinate map to another is always a differentiable function.

Orientation-based coordinates

In geometry and kinematics, coordinate systems are used to describe the (linear) position of points and the angular position of axes, planes, and rigid bodies. In the latter case, the orientation of a second (typically referred to as "local") coordinate system, fixed to the node, is defined based on the first (typically referred to as "global" or "world" coordinate system). For instance, the orientation of a rigid body can be represented by an orientation matrix, which includes, in its three columns, the Cartesian coordinates of three points. These points are used to define the orientation of the axes of the local system; they are the tips of three unit vectors aligned with those axes.

Geographic systems

Main article: Spatial reference system

The Earth as a whole is one of the most common geometric spaces requiring the precise measurement of location, and thus coordinate systems. Starting with the Greeks of the Hellenistic period, a variety of coordinate systems have been developed based on the types above, including:

• Geographic coordinate system, the spherical coordinates of latitude and longitude
• Projected coordinate systems, including thousands of cartesian coordinate systems, each based on a map projection to create a planar surface of the world or a region.
• Geocentric coordinate system, a three-dimensional cartesian coordinate system that models the earth as an object, and are most commonly used for modeling the orbits of satellites, including the Global Positioning System and other satellite navigation systems.

Position (geometry)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Position_(geometry)

Radius vector ${\displaystyle \overrightarrow{r}}$ represents the position of a point ${\displaystyle \mathrm{P}(x,y,z)}$ with respect to origin O. In Cartesian coordinate system ${\displaystyle \overrightarrow{r}=x{\hat{e}}_x+y{\hat{e}}_y+z{\hat{e}}_z.}$

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space. Its length represents the distance in relation to an arbitrary reference origin O, and its direction represents the angular orientation with respect to given reference axes. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P. In other words, it is the displacement or translation that maps the origin to P:

${\displaystyle \mathbf{r}=\overrightarrow{OP}.}$

The term position vector is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus. Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces and affine spaces of any dimension.

Relative position

The relative position of a point Q with respect to point P is the Euclidean vector resulting from the subtraction of the two absolute position vectors (each with respect to the origin):

${\displaystyle \mathrm{\Delta }\mathbf{r}=\mathbf{s}-\mathbf{r}=\overrightarrow{PQ},}$

where ${\displaystyle \mathbf{s}=\overrightarrow{OQ}}$. The relative direction between two points is their relative position normalized as a unit vector

Definition and representation

Further information: Coordinate system

Three dimensions

Space curve in 3D. The position vector r is parameterized by a scalar t. At r = a the red line is the tangent to the curve, and the blue plane is normal to the curve.

In three dimensions, any set of three-dimensional coordinates and their corresponding basis vectors can be used to define the location of a point in space—whichever is the simplest for the task at hand may be used.

Commonly, one uses the familiar Cartesian coordinate system, or sometimes spherical polar coordinates, or cylindrical coordinates:

${\displaystyle \begin{array}{rl}\mathbf{r}(t)& \equiv \mathbf{r}(x,y,z)\equiv x(t){\hat{\mathbf{e}}}_x+y(t){\hat{\mathbf{e}}}_y+z(t){\hat{\mathbf{e}}}_z\\ & \equiv \mathbf{r}(r,\theta ,\varphi )\equiv r(t){\hat{\mathbf{e}}}_r(\theta (t),\varphi (t))\\ & \equiv \mathbf{r}(r,\varphi ,z)\equiv r(t){\hat{\mathbf{e}}}_r(\varphi (t))+z(t){\hat{\mathbf{e}}}_z,\end{array}}$

where t is a parameter, owing to their rectangular or circular symmetry. These different coordinates and corresponding basis vectors represent the same position vector. More general curvilinear coordinates could be used instead and are in contexts like continuum mechanics and general relativity (in the latter case one needs an additional time coordinate).

n dimensions

Linear algebra allows for the abstraction of an n-dimensional position vector. A position vector can be expressed as a linear combination of basis vectors:

${\displaystyle \mathbf{r}=\sum _{i=1}^n{x}_i{\mathbf{e}}_i=x_1{\mathbf{e}}_1+x_2{\mathbf{e}}_2+\cdots +x_n{\mathbf{e}}_n.}$

The set of all position vectors forms position space (a vector space whose elements are the position vectors), since positions can be added (vector addition) and scaled in length (scalar multiplication) to obtain another position vector in the space. The notion of "space" is intuitive, since each x_i (i = 1, 2, …, n) can have any value, the collection of values defines a point in space.

The dimension of the position space is n (also denoted dim(R) = n). The coordinates of the vector r with respect to the basis vectors e_i are x_i. The vector of coordinates forms the coordinate vector or n-tuple (x₁, x₂, …, x_n).

Each coordinate x_i may be parameterized a number of parameters t. One parameter x_i(t) would describe a curved 1D path, two parameters x_i(t₁, t₂) describes a curved 2D surface, three x_i(t₁, t₂, t₃) describes a curved 3D volume of space, and so on.

The linear span of a basis set B = {e₁, e₂, …, e_n} equals the position space R, denoted span(B) = R.

Applications

Differential geometry

Main article: Differential geometry

Position vector fields are used to describe continuous and differentiable space curves, in which case the independent parameter needs not be time, but can be (e.g.) arc length of the curve.

Mechanics

Main articles: Newtonian mechanics, Analytical mechanics, and Equation of motion

In any equation of motion, the position vector r(t) is usually the most sought-after quantity because this function defines the motion of a particle (i.e. a point mass) – its location relative to a given coordinate system at some time t.

To define motion in terms of position, each coordinate may be parametrized by time; since each successive value of time corresponds to a sequence of successive spatial locations given by the coordinates, the continuum limit of many successive locations is a path the particle traces.

In the case of one dimension, the position has only one component, so it effectively degenerates to a scalar coordinate. It could be, say, a vector in the x direction, or the radial r direction. Equivalent notations include

${\displaystyle \mathbf{x}\equiv x\equiv x(t),r\equiv r(t),s\equiv s(t).}$

Derivatives

See also: Displacement (geometry) § Derivatives

Kinematic quantities of a classical particle: mass m, position r, velocity v, acceleration a

For a position vector r that is a function of time t, the time derivatives can be computed with respect to t. These derivatives have common utility in the study of kinematics, control theory, engineering and other sciences.

Velocity

${\displaystyle \mathbf{v}=\frac{\mathrm{d}\mathbf{r}}{\mathrm{d}t},}$

where dr is an infinitesimally small displacement (vector).

Acceleration

${\displaystyle \mathbf{a}=\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t}=\frac{{\mathrm{d}}^2\mathbf{r}}{\mathrm{d}{t}^2}.}$

Jerk

${\displaystyle \mathbf{j}=\frac{\mathrm{d}\mathbf{a}}{\mathrm{d}t}=\frac{{\mathrm{d}}^2\mathbf{v}}{\mathrm{d}{t}^2}=\frac{{\mathrm{d}}^3\mathbf{r}}{\mathrm{d}{t}^3}.}$

These names for the first, second and third derivative of position are commonly used in basic kinematics. By extension, the higher-order derivatives can be computed in a similar fashion. Study of these higher-order derivatives can improve approximations of the original displacement function. Such higher-order terms are required in order to accurately represent the displacement function as a sum of an infinite sequence, enabling several analytical techniques in engineering and physics.

Motion

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Motion

A car is moving in high speed during a championship, with respect to the ground the position is changing according to time hence the car is in relative motion

In physics, motion is when an object changes its position with respect to a reference point in a given time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of reference to an observer, measuring the change in position of the body relative to that frame with a change in time. The branch of physics describing the motion of objects without reference to their cause is called kinematics, while the branch studying forces and their effect on motion is called dynamics.

If an object is not in motion relative to a given frame of reference, it is said to be at rest, motionless, immobile, stationary, or to have a constant or time-invariant position with reference to its surroundings. Modern physics holds that, as there is no absolute frame of reference, Newton's concept of absolute motion cannot be determined. Everything in the universe can be considered to be in motion.

Motion applies to various physical systems: objects, bodies, matter particles, matter fields, radiation, radiation fields, radiation particles, curvature, and space-time. One can also speak of the motion of images, shapes, and boundaries. In general, the term motion signifies a continuous change in the position or configuration of a physical system in space. For example, one can talk about the motion of a wave or the motion of a quantum particle, where the configuration consists of the probabilities of the wave or particle occupying specific positions.

Equations of motion

${\displaystyle v}$ vs ${\displaystyle t}$ graph for a moving particle under a non-uniform acceleration ${\displaystyle a}$.

In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics.

Laws of motion

In physics, the motion of massive bodies is described through two related sets of laws of mechanics. Classical mechanics for super atomic (larger than an atom) objects (such as cars, projectiles, planets, cells, and humans) and quantum mechanics for atomic and sub-atomic objects (such as helium, protons, and electrons). Historically, Newton and Euler formulated three laws of classical mechanics:

First law:	In an inertial reference frame, an object either remains at rest or continues to move in a straight line at a constant velocity, unless acted upon by a net force.
Second law:	In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: ${\displaystyle \overrightarrow{F}=m\overrightarrow{a}}$. If the resultant force ${\displaystyle \overrightarrow{F}}$ acting on a body or an object is not equal to zero, the body will have an acceleration ${\displaystyle a}$ that is in the same direction as the resultant force.
Third law:	When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction onto the first body.

Classical mechanics

Main article: Kinematics

Classical mechanics is used for describing the motion of macroscopic objects moving at speeds significantly slower than the speed of light, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. It produces very accurate results within these domains and is one of the oldest and largest scientific descriptions in science, engineering, and technology.

Classical mechanics is fundamentally based on Newton's laws of motion. These laws describe the relationship between the forces acting on a body and the motion of that body. They were first compiled by Sir Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica, which was first published on July 5, 1687. Newton's three laws are:

1. A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force. (This is known as the law of inertia.)
2. Force (${\displaystyle \overrightarrow{F}}$) is equal to the change in momentum per change in time (${\displaystyle \frac{\mathrm{\Delta }m\overrightarrow{v}}{\mathrm{\Delta }t}}$). For a constant mass, force equals mass times acceleration (${\displaystyle \overrightarrow{F}=m\overrightarrow{a}}$ ).
3. For every action, there is an equal and opposite reaction. (In other words, whenever one body exerts a force ${\displaystyle \overrightarrow{F}}$ onto a second body, (in some cases, which is standing still) the second body exerts the force ${\displaystyle -\overrightarrow{F}}$ back onto the first body. ${\displaystyle \overrightarrow{F}}$ and ${\displaystyle -\overrightarrow{F}}$ are equal in magnitude and opposite in direction. So, the body that exerts ${\displaystyle \overrightarrow{F}}$ will be pushed backward.)

Newton's three laws of motion were the first to accurately provide a mathematical model for understanding orbiting bodies in outer space. This explanation unified the motion of celestial bodies and the motion of objects on Earth.

Relativistic mechanics

Modern kinematics developed with study of electromagnetism and refers all velocities ${\displaystyle v}$ to their ratio to speed of light ${\displaystyle c}$. Velocity is then interpreted as rapidity, the hyperbolic angle ${\displaystyle \phi }$ for which the hyperbolic tangent function ${\displaystyle \tanh \phi =v÷c}$. Acceleration, the change of velocity over time, then changes rapidity according to Lorentz transformations. This part of mechanics is special relativity. Efforts to incorporate gravity into relativistic mechanics were made by W. K. Clifford and Albert Einstein. The development used differential geometry to describe a curved universe with gravity; the study is called general relativity.

Quantum mechanics

Quantum mechanics is a set of principles describing physical reality at the atomic level of matter (molecules and atoms) and the subatomic particles (electrons, protons, neutrons, and even smaller elementary particles such as quarks). These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation energy as described in the wave–particle duality.

In classical mechanics, accurate measurements and predictions of the state of objects can be calculated, such as location and velocity. In quantum mechanics, due to the Heisenberg uncertainty principle, the complete state of a subatomic particle, such as its location and velocity, cannot be simultaneously determined.

In addition to describing the motion of atomic level phenomena, quantum mechanics is useful in understanding some large-scale phenomena such as superfluidity, superconductivity, and biological systems, including the function of smell receptors and the structures of protein.

Orders of magnitude

Humans, like all known things in the universe, are in constant motion; however, aside from obvious movements of the various external body parts and locomotion, humans are in motion in a variety of ways that are more difficult to perceive. Many of these "imperceptible motions" are only perceivable with the help of special tools and careful observation. The larger scales of imperceptible motions are difficult for humans to perceive for two reasons: Newton's laws of motion (particularly the third), which prevents the feeling of motion on a mass to which the observer is connected, and the lack of an obvious frame of reference that would allow individuals to easily see that they are moving. The smaller scales of these motions are too small to be detected conventionally with human senses.

Universe

Spacetime (the fabric of the universe) is expanding, meaning everything in the universe is stretching, like a rubber band. This motion is the most obscure as it is not physical motion, but rather a change in the very nature of the universe. The primary source of verification of this expansion was provided by Edwin Hubble who demonstrated that all galaxies and distant astronomical objects were moving away from Earth, known as Hubble's law, predicted by a universal expansion.

Galaxy

The Milky Way Galaxy is moving through space and many astronomers believe the velocity of this motion to be approximately 600 kilometres per second (1,340,000 mph) relative to the observed locations of other nearby galaxies. Another reference frame is provided by the Cosmic microwave background. This frame of reference indicates that the Milky Way is moving at around 582 kilometres per second (1,300,000 mph).

Sun and Solar System

See also: Planetary motion

The Milky Way is rotating around its dense Galactic Center, thus the Sun is moving in a circle within the galaxy's gravity. Away from the central bulge, or outer rim, the typical stellar velocity is between 210 and 240 kilometres per second (470,000 and 540,000 mph). All planets and their moons move with the Sun. Thus, the Solar System is in motion.

Earth

The Earth is rotating or spinning around its axis. This is evidenced by day and night, at the equator the earth has an eastward velocity of 0.4651 kilometres per second (1,040 mph). The Earth is also orbiting around the Sun in an orbital revolution. A complete orbit around the Sun takes one year, or about 365 days; it averages a speed of about 30 kilometres per second (67,000 mph).

Continents

The Theory of Plate tectonics tells us that the continents are drifting on convection currents within the mantle, causing them to move across the surface of the planet at the slow speed of approximately 2.54 centimetres (1 in) per year. However, the velocities of plates range widely. The fastest-moving plates are the oceanic plates, with the Cocos Plate advancing at a rate of 75 millimetres (3.0 in) per year and the Pacific Plate moving 52–69 millimetres (2.0–2.7 in) per year. At the other extreme, the slowest-moving plate is the Eurasian Plate, progressing at a typical rate of about 21 millimetres (0.83 in) per year.

Internal body

The human heart is regularly contracting to move blood throughout the body. Through larger veins and arteries in the body, blood has been found to travel at approximately 0.33 m/s. Though considerable variation exists, and peak flows in the venae cavae have been found between 0.1 and 0.45 metres per second (0.33 and 1.48 ft/s). additionally, the smooth muscles of hollow internal organs are moving. The most familiar would be the occurrence of peristalsis, which is where digested food is forced throughout the digestive tract. Though different foods travel through the body at different rates, an average speed through the human small intestine is 3.48 kilometres per hour (2.16 mph). The human lymphatic system is also constantly causing movements of excess fluids, lipids, and immune system related products around the body. The lymph fluid has been found to move through a lymph capillary of the skin at approximately 0.0000097 m/s.

Cells

The cells of the human body have many structures and organelles that move throughout them. Cytoplasmic streaming is a way in which cells move molecular substances throughout the cytoplasm, various motor proteins work as molecular motors within a cell and move along the surface of various cellular substrates such as microtubules, and motor proteins are typically powered by the hydrolysis of adenosine triphosphate (ATP), and convert chemical energy into mechanical work. Vesicles propelled by motor proteins have been found to have a velocity of approximately 0.00000152 m/s.

Particles

According to the laws of thermodynamics, all particles of matter are in constant random motion as long as the temperature is above absolute zero. Thus the molecules and atoms that make up the human body are vibrating, colliding, and moving. This motion can be detected as temperature; higher temperatures, which represent greater kinetic energy in the particles, feel warm to humans who sense the thermal energy transferring from the object being touched to their nerves. Similarly, when lower temperature objects are touched, the senses perceive the transfer of heat away from the body as a feeling of cold.

Subatomic particles

Within the standard atomic orbital model, electrons exist in a region around the nucleus of each atom. This region is called the electron cloud. According to Bohr's model of the atom, electrons have a high velocity, and the larger the nucleus they are orbiting the faster they would need to move. If electrons were to move about the electron cloud in strict paths the same way planets orbit the Sun, then electrons would be required to do so at speeds that would far exceed the speed of light. However, there is no reason that one must confine oneself to this strict conceptualization (that electrons move in paths the same way macroscopic objects do), rather one can conceptualize electrons to be 'particles' that capriciously exist within the bounds of the electron cloud. Inside the atomic nucleus, the protons and neutrons are also probably moving around due to the electrical repulsion of the protons and the presence of angular momentum of both particles.

Light

Main article: Speed of light

Light moves at a speed of 299,792,458 m/s, or 299,792.458 kilometres per second (186,282.397 mi/s), in a vacuum. The speed of light in vacuum (or ${\displaystyle c}$) is also the speed of all massless particles and associated fields in a vacuum, and it is the upper limit on the speed at which energy, matter, information or causation can travel. The speed of light in vacuum is thus the upper limit for speed for all physical systems.

In addition, the speed of light is an invariant quantity: it has the same value, irrespective of the position or speed of the observer. This property makes the speed of light c a natural measurement unit for speed and a fundamental constant of nature.

In 2019, the speed of light was redefined alongside all seven SI base units using what it calls "the explicit-constant formulation", where each "unit is defined indirectly by specifying explicitly an exact value for a well-recognized fundamental constant", as was done for the speed of light. A new, but completely equivalent, wording of the metre's definition was proposed: "The metre, symbol m, is the unit of length; its magnitude is set by fixing the numerical value of the speed of light in vacuum to be equal to exactly 299792458 when it is expressed in the SI unit m s⁻¹." This implicit change to the speed of light was one of the changes that was incorporated in the 2019 revision of the SI, also termed the New SI.

Superluminal motion

See also: Superluminal motion

Some motion appears to an observer to exceed the speed of light. Bursts of energy moving out along the relativistic jets emitted from these objects can have a proper motion that appears greater than the speed of light. All of these sources are thought to contain a black hole, responsible for the ejection of mass at high velocities. Light echoes can also produce apparent superluminal motion. This occurs owing to how motion is often calculated at long distances; oftentimes calculations fail to account for the fact that the speed of light is finite. When measuring the movement of distant objects across the sky, there is a large time delay between what has been observed and what has occurred, due to the large distance the light from the distant object has to travel to reach us. The error in the above naive calculation comes from the fact that when an object has a component of velocity directed towards the Earth, as the object moves closer to the Earth that time delay becomes smaller. This means that the apparent speed as calculated above is greater than the actual speed. Correspondingly, if the object is moving away from the Earth, the above calculation underestimates the actual speed.

Types of motion

• Simple harmonic motion – motion in which the body oscillates in such a way that the restoring force acting on it is directly proportional to the body's displacement. Mathematically Force is directly proportional to the negative of displacement. Negative sign signifies the restoring nature of the force. (e.g., that of a pendulum).
• Linear motion – motion that follows a straight linear path, and whose displacement is exactly the same as its trajectory. [Also known as rectilinear motion]
• Reciprocal motion
• Brownian motion – the random movement of very small particles
• Circular motion
• Rotatory motion – a motion about a fixed point. (e.g. Ferris wheel).
• Curvilinear motion – It is defined as the motion along a curved path that may be planar or in three dimensions.
• Rolling motion – (as of the wheel of a bicycle)
• Oscillatory – (swinging from side to side)
• Vibratory motion
• Combination (or simultaneous) motions – Combination of two or more above listed motions
• Projectile motion – uniform horizontal motion + vertical accelerated motion

Fundamental motions

• Linear motion
• Circular motion
• Oscillation
• Wave
• Relative motion
• Rotary motion