# Motion

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A motorcyclist doing a wheelie- representing motion

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

If an object is not changing relative to a given frame of reference, the object is said to be at rest, motionless, immobile, stationary, or to have a constant or time-invariant position with reference to its surroundings. As there is no absolute frame of reference, absolute motion cannot be determined.[1] Thus, everything in the universe can be considered to be in motion.[2]: 20–21

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 positions 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 probabilities of the wave or particle occupying specific positions.

## Laws of motion

In physics, the motion of massive bodies is described through two related sets of laws of mechanics. Classical mechanics for superatomic (larger than atomic) 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: F = ma. If the resultant force F acting on a body or an object is not equal to zero, the body will have an acceleration a which 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 on the first body.

### Classical mechanics

Classical mechanics is used for describing the motion of macroscopic objects, 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, 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 is equal to the change in momentum (mv) per change in time. For a constant mass, force equals mass times acceleration (F = ma).
3. For every action, there is an equal and opposite reaction.
i.e. whenever one body exerts a force F onto a second body, (in some cases, which is standing still) the second body exerts the force −F back onto the first body. F and −F are equal in magnitude and opposite in direction. So, the body which exerts F will be pushed backward.[3]

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.

### Equations of motion

Translational motion

In translational motion, the driving force F is counterbalanced by a resisting force Fr set up by the driven machine and by an inertia force Ma arising from the change in speed, or

${\displaystyle {\vec {F}}-{\vec {Fr}}=M{\vec {a}}=M{\operatorname {d} \!{\vec {v}} \over \operatorname {d} \!{\vec {t}}}}$ (1)

where the mass M is expressed in kg, the velocity v in m/sec, the acceleration a in m/sec2, and the force F in newtons (N).[4]

Oscillatory motion

A motion repeating itself is referred to as periodic or oscillatory motion. An object in such motion oscillates about an equilibrium position due to a restoring force or torque. Such force or torque tends to restore (return) the system toward its equilibrium position no matter in which direction the system is displaced.[5]

Rotational motion

In rotational motion, the driving torque TM (usually developed by an electric motor) is counterbalanced by a resisting torque TL (usually developed by the load and referred to as the motor shaft) and by an inertia or dynamic torque J dω/dt,

${\displaystyle T_{M}-T_{L}=J\operatorname {d} \!\omega /\operatorname {d} \!t}$ (2)

where the inertia J is expressed in kg*m2. It is sometimes called flywheel torque or moment and T is the torque in N*m. The signs to be associated with TM and TL in Eq. (2) depend on the regime of operation of the driving motor and the nature of the load torque.[4]

Uniform motion:

When an object moves with a constant speed in a particular direction at regular intervals of time it is known as uniform motion. For example: a bike moving in a straight line with a constant speed. Here the value of acceleration will be zero.

Equations of uniform motion:

If ${\displaystyle \mathbf {v} }$ = final and initial velocity, ${\displaystyle t}$ = time, and ${\displaystyle \mathbf {s} }$ = displacement, then:

${\displaystyle \mathbf {s} =\mathbf {v} t}$ (3)

If ${\displaystyle \mathbf {v} }$ is final velocity and ${\displaystyle \mathbf {u} }$ is initial velocity, ${\displaystyle \mathbf {a} }$ is acceleration throughout the time(${\displaystyle t}$), and ${\displaystyle \mathbf {s} }$ = displacement, then:

${\displaystyle \mathbf {v} =\mathbf {u} +\mathbf {a} t}$

${\displaystyle \mathbf {s} =\mathbf {u} t+1/2\mathbf {a} t}$2

${\displaystyle \mathbf {v^{2}} -\mathbf {u^{2}} =2\mathbf {a} s}$

Non-uniform motion:

When an object moves with a different or variable velocity is called non-uniform motion at a regular time interval. An object covers different distances in an equal time interval. Here acceleration has a non-zero value. Example: A running horse.

There are two types of non-uniform motion with respect to acceleration:

Uniformly accelerated non-uniform motion: When objects move with different velocities in an equal time interval and acceleration is constant throughout the time interval. This means the velocity of an object will change at a constant rate in a given time interval. Example: Free fall of an object due to gravity (acceleration: due to gravity 9.8 m/s2 throughout the time interval).

Here acceleration is non-zero but constant.

Non-uniformly accelerated non-uniform motion: When objects move with different velocities in an equal time interval and acceleration is variable throughout the time interval. This means the velocity of an object will not change at a constant rate. Example: Driving a car with different velocities at different time intervals.

Here acceleration is non-zero but variable.

### Relativistic mechanics

Modern kinematics developed with study of electromagnetism and refers all velocities v to their ratio to speed of light c. Velocity is then interpreted as rapidity, the hyperbolic angle φ for which the hyperbolic tangent function tanh φ = v/c. Acceleration, the change of velocity, 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.[6]

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.[7]

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.[8]

## List of "imperceptible" human motions

Humans, like all known things in the universe, are in constant motion;[2]: 8–9  however, aside from obvious movements of the various external body parts and locomotion, humans are in motion in a variety of ways which 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 which would allow individuals to easily see that they are moving.[9] 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.[10]

### 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).[11][failed verification]

### Sun and solar system

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).[12] All planets and their moons move with the sun. Thus, the solar system is moving.

### 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).[13] 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).[14]

### 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.[15][16] 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[17] 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 constantly 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).[18] 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).[19] 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.[20]

### Cells

The cells of the human body have many structures which move throughout them. Cytoplasmic streaming is a way in which cells move molecular substances throughout the cytoplasm,[21] 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.[22] Vesicles propelled by motor proteins have been found to have a velocity of approximately 0.00000152 m/s.[23]

### 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 which 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.[24]

### Subatomic particles

Within each atom, electrons exist in a region around the nucleus. 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 '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 which 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.[25] 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.[26]

## 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 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.

## References

1. ^ Wahlin, Lars (1997). "9.1 Relative and absolute motion" (PDF). The Deadbeat Universe. Boulder, CO: Coultron Research. pp. 121–129. ISBN 978-0-933407-03-9. Retrieved 25 January 2013.
2. ^ a b Tyson, Neil de Grasse; Charles Tsun-Chu Liu; Robert Irion (2000). One Universe : at home in the cosmos. Washington, DC: National Academy Press. ISBN 978-0-309-06488-0.
3. ^ Newton's "Axioms or Laws of Motion" can be found in the "Principia" on p. 19 of volume 1 of the 1729 translation.
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6. ^ The Feynman Lectures on Physics Vol. I Ch. 38: The Relation of Wave and Particle Viewpoints
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